what type of fitting am I talking about?

Hey ya'll, I'm Eric. Just bought my first house, so you'll prob. be seeing me a lot. Got a question about what fitting I need, and If what I have in mind is appropriate. My down stairs laundry room shares a wall with my down stairs bathroom. above the laundry room is the upstairs master bath. so this wall has plenty of plumbing in it. the previous occupants had the washer drain (p trap up) out side of the wall, along with several feet of both the hot and cold water with tee's and another couple feet then another valve. 2 hot valves, 2 cold valves, and plumbing all over outside the wall. I have the water situation under control, I just need to know what kind of fitting to use to add a 3x2 wye to one of the vertical stacks. I cannot spread the 3" apart to get a normal slip joint in there. Is there some cool fittings just for this application? I have attached a rough sketch of my situation. please let me know if you see any problems with my idea. Thanks

First, a wye is not the proper fitting. Needs to be a sanitary tee.

You need to vent the relocated WM stand pipe. See the part that goes up from where it connects to the drain going down? You need something similar unless, that 3" pipe is a vent for things below. Once a drain, always a drain...once a vent, always a vent.

I would guess that the stack on the left is a vent for the plumbing on the first floor. That's why you never hear water going down it. That is also why the washer is on the wet stack on the right. They knew what they were doing.

The pipe you want to use is the vent for the downstairs, which means "legally" you cannot use it, OR the smaller line for a washer drain. The fact that the smaller pipe connects to the larger one is a positive indication that the large pipe IS a vent not a drain.