Your best bet it to cut out the lower connection where the two 3" lines combine and use a double fitting there. Essentially making it a three way connection. The sink will need a drain low enough to be usable anyway. If you need to slighty raise the tee for the washer, that's doable.
The vent above the washer can be tapped into for the sink vent.
It looks like a 22 bend below the wye. If you need to remove the pipe from the hub, you can use a rambit on a drill to remove it.