[baltdiy]

This is my first post and I am not sure about the best way to do this but here it goes.

As part of the reconfiguration of our laundry room, we would like to rotate our washing machine hookups 90° (to the perpendicular wall shown in the picture). However I am not sure how to run the new drain line. I have attached a picture which I hope helps. The current drain is 1 1/2 with an s trap that ties into the kitchen sink drain through a wye right at the 3" stack. Approx. 5' up from where that ties into the 3" stack is a drain and trap for a 2nd floor bathroom sink and above that is the vent for 3" stack. In the picture you can see the drain for the 1st floor bathroom sink that is on the other side of the wall. In the basement (right below the section shown in the picture) the 3" main bends 90°, joins the drain for the 1st floor bathroom toilet, and runs horizontally ~5' where it ties into a separately vented stack (for the remaining upstairs shower sinks and toilets). That pipe then exits the house. My question is whether I should 1.) tie the new 2" washing machine drain (after the p trap) into the existing kitchen drain line or 2.) replace the wye that serves the bathroom sink with a double wye and then tie the new washing machine drain into that.
I feel like option 2 is better but am not sure. If option 2 is the way to go, I assume I will use at least 1 fernco type fitting to attach the new double wye and that I can just cap off the old washing machine drain. Also I wasn't going to vent the new washing machine drain even though it will have an almost horizontal (sloped at 1/4" per ft) 90° bend after the p trap since it will be within 6 feet of the 3" main.
I should also say that I am moving the wall shown in the picture out 1 1/2" as the plane of the current wall is slightly behind that of the vertical 3/4 copper line. The new washing machine box will be located in a soon to be framed 2x6 wall (right side of picture)
I hope that makes sense. Any advice would be welcome and greatly appreciated. Thank you.