Adding utility sink drain

[Ryo]

Forgive my lack of plumbing knowledge, I've never needed to plan anything before I've only ever removed and replaced.
I'm trying to add a utity sink where my washer used to be, a city inspector told me I was ok to tie into the washer drain between it's p-trap and the vent, upon cutting the wall open there really isn't much room so I'm trying to figure out the best way to go about this. Was considering moving the p-trap for the washer drain all the way to the left to allow me to use a wye to tie into the line but I'm not sure there's enough room??
Would I be better off trying to tie into the other sink drain? I can't think of a good way to go about that.
Maybe a double 90° elbow to tie into that other sink drain? Would that be a proper horizontal T to use there?

I'm attaching a picture, in the pic is the washer drain and also the drain for the sink on the other side of the wall, venting is assumed to be to the right past that stud (I can remove more drywall if needed but I need the drain line to go into the wall here.)

 

[Terry]

You will need to remove more drywall. There is almost nothing to work with there.

 

[Sponsor]

 

[Ryo]

You will need to remove more drywall. There is almost nothing to work with there.

I figured that was going to be the case. Here's to the right of that stud. There's the drain/vent as expected. Also not much room to work with.

 

[Ryo]

Well I ended up deciding that my intro into plumbing projects probably shouldn’t be this one simply because the lack of room to work and I hired a professional. pic attached of the solution, he started notching out the stud to make room for the new connection when he discovered the stud was notched on both sides and wasn’t supporting any weight. So it was removed entirely.
Maybe this will help someone in the future.

 

[Terry]

You do know that won't work. He's running the washer right by the drain for the sink. It will siphon.
And he even raised the height on it, even worse. Who was that guy?

Not perfect, but the laundry tray gets it's own vent,
The lav wet vents the washer, which is not what we normally do, but a fixture with a 1.25" drain going into a 2" above the washer is way, way better than running a pumped 2" lines past a 1.5" drain that was raised in a way that ruins the venting .

Sorry I didn't draw this sooner.