Other options I explored and rejected:

• Dump the line into the sink or bathtub instead. Pretty good option, but I'm like 90% sure the kids would drink a bunch of dehumidifier water if I did this. There's no way to keep the line out of reach given the geometry of the bathrooms.
• Dump it into the toilet. Reasonable, but could possibly cause mysterious flushes at random times.
• Dump the line into the toilet tank. This has an unlikely-but-not-impossible failure mode of overflowing the tank.

My terminology might be wrong throughout this but a couple thoughts:

1. I don't know about deHum pumps and if they're required to be air-gapped. Regardless of if they are or aren't, you could:
2. Tee off the drain pipe, such that the new stuff uses the same trap. Create a vertical standpipe, similar to a laundry room washer drain line. air-gap the dehum line over the top of the standpipe if air gap is required, or just shove the line into the standpipe a few inches if air gap is not required.
3. Put a leak sensor in the cabinet.

Since there's no fresh water supply to the dehumidifier I don't think there's much benefit to an air gap, as there's no way backflow could ever contaminate a supply line. A clogged sink drain could possibly drain sink water out through the dehumidifier bucket, but the top of the drain line is only ~1"-2" below the top of the sink so it would overflow the basin onto the floor before very long anyway.

I do already have some 1/4" Check Valves like these, so I could add them to the drain lines, although a highly scientific "blow into the fitting" test makes it seem like the, uh, "forward resistance" of the fitting (I guess it's a threshold pressure called the "cracking pressure") is also pretty high and I'm not sure the dehumidifier pump could overpower it. Some commenter on Amazon says those crack at 5-10 PSI. I can't find a rating for the dehumidifier pump, but "10 PSI" ~= "23 Feet of Water" and that seems optimistic since I wouldn't usually expect a dehumidifier to need to pump water up two stories to get to a drain. Here's a special high-spec 1/4" check valve that cracks at 1/3 PSI, but they're $10 each, which makes my ridiculous $80 of plumbing into $90 of plumbing. Of course, that's still a lot cheaper than a new floor.

Tee off the drain pipe, such that the new stuff uses the same trap...

Yeah, that's what I've got so far -- here are a couple photos:

Create a vertical standpipe...

I could do this, but the top of the vanity is a one-piece porcelain sort of thing so I think I'd have to maybe come off the tee with flexible dishwasher drainpipe, get another adapter to convert that into something rigid (PVC?) for the standpipe, and then drill through the side of the vanity, possibly reinforce it since it's like 1/4" ply, and then maybe do some kind of PVC flange fitting and run the standpipe up between the sink and toilet, which is probably another $40 of parts and a big hole in the vanity. And the wall is tile up to maybe 4' so I can't easily do anything in the wall without turning it into a retiling project (again).

I suppose I could put a tee in the 1/4" line, but since the dehumidifier side is pressurized by a pump I think any standpipe approach ultimately only makes it slightly more difficult for the dehumidifier to pump water all over the floor in the event of drain clog.

Put a leak sensor in the cabinet.

The cost of replacing the whole floor might be lower than the cost of waking everyone up in the middle of the night with an alarm, but if I had a leak sensor that just kills the power to the dehumidifier and makes a very quiet light flash, that would probably be a net benefit even if it had occasional false alarms. It looks like these are commercially available (Leak Detector with Power Cutoff) for about $80 (or maybe more cheaply with separate Smart Home "Leak Detector" and "Power Cutoff" components) but I'm pretty sure I could build one myself inside of 12 months for not more than $200 in parts.

A few more thoughts:

1. Plumbers HATE those flexible traps. High failure rate from what I regularly read on /r/plumbing.
2. The trap pictured is effectively the entirety of that flexible pipe. It is arguably more of an S-trap than a P-trap because you don't have any meaningful section of horizontal fall. You are at higher risk of siphoning out the water from that trap, making for a smelly situation.
3. Have you tested the dehumidifier pump's GPM output? We have a water softener that does a backwash cycle that has a super high GPM output (pressurized by the main water supply, I believe). This drains through an air gap into a standpipe.

I can't see a way to make the trap be any less garbage than it is because the 4" flanged tailpipe (the shortest flanged 1-1/4" tailpipe I could find) plus an additional 8" of tailpipe underneath it (the only 1-1/4" branch tailpipe I could find, which is only available with a slip fitting) means that the bottom of the lower tailpipe is super low. It looks like I left an extra 6" of flexible pipe on the drain side for fun, but that's just the rigid bottom of the tailpipe plus the minimum bend radius without making the flexible pipe start to crimp -- the bottom of the tailpipe is like 1-1/2" below the black plastic retainer clip.

I'd love to just buy this $15 tailpiece except maybe 6" long and then connect it to a normal p-trap (perhaps -- there are other reasons this is complicated in this particular application), but if you want that $15 part in 1-1/4" it seems like you've broken a secret rule of plumbing and are some kind of loon.

The best remedy I can come up with is that I could cut one or both tailpipes to shorten them, but I'm not set up to cleanly cut thin-walled metal pipe and I'm worried the cut ends might become more susceptible to corrosion, since they wouldn't be plated and would be in contact with water, so I'm not sure if this would improve anything even if I managed to make the cuts cleanly.

The dehumidifier could possibly siphon the p-trap in an extreme case (sink drain closed, wall drain clogged?), but it would just siphon it into the already-pretty-gross dehumidifier bucket, which is large enough to hold the contents of the p-trap several times over. I can't immediately come up with a scenario where the p-trap is repeatedly refilled and siphoned out before someone fixes some link in the chain. These sinks are on the 2nd/3rd floors so even sewer backpressure would overflow something on the 1st floor before they could be affected.

Have you tested the dehumidifier pump's GPM output?

It's barely a trickle, like a gallon an hour or something in that realm. The unit is rated for a maximum of 50 pints/day so a ~1/200th-GPM pump could keep up with it. In practice, it does more like ~1-2 pints/day.

¯\_(ツ)_/¯

Here is my bathroom sink. The right-most pipe coming out of the wall is the condensate drain from HVAC. The tailpiece is most definitely 1 1/4 and the rest of the piping is 1 1/2, at least to the naked eye.

Maybe something like this could work?

(You don't actually need a leak detector, I think there's enough absorbent material underneath the sink to last a long while before it damages the floor)

:)

sorry, needed a bit of a humor outlet today!

...there's enough absorbent material underneath the sink...

...the rest of the piping is 1 1/2...

Hmmmm....

I did try to come up with an approach using a 1-1/4"-to-1-1/2" reducer ("unreducer"? "increaser"?) but the wall drainpipe is also 1-1/4" so I need to go from 1-1/4" to 1-1/2", branch off, then go back to 1-1/4" before we get to the wall. It seemed hard to do this without having more total length than the mess I ended up with, but taking another look at it maybe this would actually work fine:

• The existing 4" flanged tailpiece.
• 1-1/4" Slip Joint to 1-1/2" PVC Adapter to get up to 1-1/2".
• 1-1/2" Appliance Wye or any other 1-1/2" branch/wye/tee since there's plenty of room to figure things out on the drain line side above the branch.
• 1-1/2" to 1-1/4" Reducing Coupling to get back to 1-1/4".

I suspect this isn't that much shorter than the 8" branch tailpiece, but it's probably a bit shorter, and the 4" tailpiece could sit further down in the assembly, and it costs about $8 instead of $37, and it doesn't look like quite as much of a pile of garbage, so maybe I'll give this a shot.

... condensate drain ...

Oh! I've got a concern troll for this one -- do you have an inline condensate neutralizer?

If you don't, all your pipes are already dead!

all my drains are belong to PVC

Couple of years ago the furnace wasn't working so well. Light comes on, three reds. Pressure switch stuck open. I take off a panel, pull the pressure switches. The contacts close properly. No clue what's wrong. Call an HVAC guy. He's pretty busy. No problem, we got plenty of sweaters. Ha. He makes it out early the next week.

Barely has to look at the unit. "Bad board," he says, "see it all the time. Install a newfangled smart thermostat? Two wire?"

"Yeah," I say. "How'd you know?"

"That'll do it. Fries these boards. No problem, got the part in the van."

He replaces the board. Furnace starts up on the first try. ($300)

"Might want to add a condensate neutralizer," he says. "The runoff is acid. Remember that Aliens movie? It chews through the old iron pipes deep in the earth. Big problem if that happens, gotta just about throw away the whole house. Maybe the whole neighborhood."

"Smart fellow," I think to myself. "Glad I gave him a call."

I drill a bunch of holes in the house. Some of them are good enough. Run 5-conductor thermostat wire through the wall, down into the garage. Don't hit any water or power on the way down. Order a condensate neutralizer and a nice box for it ($200). Drill more holes in the exterior of the house and install it. Next cold day comes around, I test the pH. Neutral. Looks like it's working. Algae stops growing on the back patio where the condensate flows down to the drain. Glad I gave that guy a call.

Maybe I should trust the professionals a little more, I was way out of my depth on this one.

A year passes. Furnace isn't starting up. Kicks on after a while. Bad board again, right? Order a replacement part ($100). Furnace struggles a bit but makes it through to spring. Board stays in the box on a shelf. Little bit of peace of mind, can't put a price on that.

Spring passes. Summer passes. Winter again, just now. Furnace isn't starting up. Dead quiet. Light comes on, three reds. Pressure switch stuck open. Time to shine. I swap the board.

Light comes on, three reds. Pressure switch stuck open.

Oof.

Guess I gotta call that guy again. Good guy to call.

Go through the motions so I'm not wasting his time. Pull the pressure switches. Really don't want to embarrass myself in front of a professional. Contacts close properly, they're fine. Can I rig up something to make dead sure? Contacts close properly. How risky is it to run wires out of the combustion chamber and try to press something at the right time? Contacts close properly.

No. They don't close properly. Jiggle the switch a little bit and the resistance is 300 Ω fully closed. Jiggle it a little more and it closes properly.

Part is out of production. Maybe it was unreliable. Maybe I just got unlucky. There's a direct replacement. Order the switch ($20), arrives the next day. Furnace starts up on the first try.

Should have known better than to trust a professional.

If the small pipe needs to drain into the big one, how about taking a large pvc end-cap, drilling a 1/4" hold and forcing the smaller pipe in it? Maybe seal the whole thing with some silicone.

If the small pipe needs to drain into the big one, how about taking a large pvc end-cap, drilling a 1/4" hold and forcing the smaller pipe in it?

I think that'd work fine, but then I'd still need to connect the PVC end-cap to the main drainline and the only tee I could find originally was that $37 one with a 7/8" inlet with no threads, which I don't know how to join to PVC.

If I redo it with the PVC parts above, using an end-cap with a hole in it and a normal tee/wye (instead of the "Appliance Wye") seems reasonable.

Things I've figured out:

1-1/2" Pipe

The lingua franca of (American) drain pipe appears to be 1-1/2", and a general strategy is to convert to 1-1/2" and implement all features in 1-1/2", returning to 1-1/4" only if/when required.

Note that 1-1/2" PVC drain pipe is not the same as 1-1/2" regular old PVC pipe. 1-1/2" drain pipe has an OD of 1.5". Normal schedule 40 1-1/2" PVC has an OD of 1.9". If you wanted to use regular PVC, you would need a "Hub" adapter like 1-1/2 in. PVC DWV Hub x Slip-Joint Trap Adapter.

Adapters

It's generally not trivial to find a 1-1/4" to 1-1/2" adapter because this part is usually unnecessary: many 1-1/2" fittings include a 1-1/4" to 1-1/2" reducing washer. For example, this 1-1/2 in. x 12 in. White Plastic Slip-Joint Sink Drain Extension Tube can attach to 1-1/4" or 1-1/2" drainpipe, by using one of the two different washers that come in the bag.

Cutting Tailpieces

This is no surprise, but you can cut plastic tailpieces to whatever size you want, e.g. with a tool like 1-1/4 in. AND 1-1/2 in. PTEC 3000 Versatile Thin Wall PE, PP, PVC Plastic Tubing Cutter.

You can probably also cut metal tailpieces, e.g. this plumber who has a website says that's fine. My concern was that you'd be cutting through the chrome and maybe exposing the interior metal to corrosion, but it seems like chromed plumbing fittings are generally chromed brass anyway.

Flexible Fittings

The SimpleDrain flexible P-Traps I linked above are still working fine, but a separate Form N Fit 1-1/4 in. White Plastic Slip-Joint Sink Drain Tailpiece Extension Tube in a different light-duty sink that essentially drains only soap, water, and coffee became completely clogged with black sludge in less than two years.

PVC Flanged 1-1/4" Tailpieces

As far as I can tell, these just don't exist.

What I Should Have Done

The general outline of the right way to do this is probably:

This seems like a much more reasonable bill of materials, and shifts much of the cost to the specialty part.