I found a leak under my kitchen sink coming from a hole in the brass or copper pipe leading into the wall. Threw a no-hub coupler over the hole temporarily which made the hole bigger. Poked around and suspected it was also leaking in the wall. And of course it was...
Replacing this section with PVC is where I'm at (let me know if I'm wrong), but how would I connect it to the fitting circled in red?
The right fix is to replace pipes. That's relatively straightforward if there's a basement under this sink; the question then is just how much to replace and what with.
The wrong fix is to cut out and replace just the part that is currently leaking until you can afford the right fix.
The wronger fix is to slap epoxy putty around it until you can afford the wrong fix, trying to leave enough uncovered area for easy later disassembly ...
Frankly, I'd consider getting a plumber in and having that whole drain redone back to where it's solid, and while you have her on site have her look for other needed work. It's cheaper to do the work on a smaller number of visits, not to mention reducing risk of finding the next leak the hard way. I can handle plumbing but this looks like more than I would want to deal with and I'd want an experienced eye.
Note that the pipe failing here in the way it has suggests that someone has been clearing clogs with excess chemistry and)or excess force. It that was a prior occupancy you can't do much about it. If it was you, consider getting a good hand-cranked drain auger and/or setting aside a small plunger for use with non-toilet drain clogs. And not putting larger/oilier things down the drain, and possibly getting a better sink strainer.
You can probably safely assume that the damage to the horizontal section of pipe goes all the way to the tee fitting, or at least close enough to make no difference. Because of that, you'll need to replace the fitting as well.
Luckily, since the damage appears to be corrosion from whatever was sitting/flowing in the pipe, your vertical pipes probably don't need to be replaced yet.
Two things that work in your favor are the fact that plastic (ABS and PVC) DWV pipes are made in CTS (copper tubing size), and that DWV pipes aren't under pressure, which widens your choice of fittings. I would assume that you have a 1 1/2" drain stub, a 1 1/2" vent, and a 2" drain stack, but you should measure to be sure. Outside diameters of plastic drain pipes will be the same as the outside diameter of the existing copper.
What I would do here is cut at the top and bottom of the brass tee, then replace the tee and piping all the way to the sink with ABS drain pipe and fittings. You can use rubber couplings and short sections of pipe to attach to the two vertical sections of existing pipe, then use glued ABS fittings to get to your sink.
I wouldn't bother with expensive push-to-connect fittings (commonly branded as SharkBite) here. Even though they are easy to use, they are designed for pressure applications, which is unnecessary for drains.
