Can I combine the laundry sink 2" drain, with the clothes washer
drain shower drain or should it have it's own 2" pipe going to the 3"?

Does the part of your question "clothes washer drain shower drain" mean you
have a shower tied into your washer drain somehow ?

If so, I wouldn't ADD a laundry sink to it as well.

Combining a washer drain with a laundry sink drain (no shower) is done all
the time.