If you want a sink to the right of the washer standpipe, I would add a tee below the tee for the washer drain, and run below to the other side.
Then you would use a long turn 90 el, up to a santee fitting for the sink drain.
The vent above the tee would continue up and could be turned again at 42" and revent with the other vents, or continue straight up through the roof.
As for the top drawing, the wye on the vent, though it looks clean and all, does not meet the purpose of using wye fittings below grade.
The assumption is that water goes down the vents and needs to drain properly through the fittings.
If that is the case, it's obvious that the wye is backwards. The wye should be flipped around and fittings used to bring the pipe toward the wall.
If left as is, the next owner of the home adds plumbing mistakenly to the vent. The waste has to drop down through the wye toward the shower p-trap and then make a U-turn on itself to thead down the drain. Forget about running a snake down that thing.
Your're thinking hard, but not getting it yet.