Her mental state is not yours to own, particularly while separated. Depending on the therapist, many are quick to advise divorcing and moving forward to combat unhappiness which is not DB. It can do more harm to your marriage than good. If she wants to see a therapist that is up to her, you should stay out of it. Suggesting it to her may imply to her that you think she is broken in some way, just stay away from it.
You may choose to make MC a condition for having her move back in (or start staying overnight), but YOU should meet with several MC's alone and prep them on what you hope to accomplish. Do not just jump in the pool with an unknown MC and trust your goals will be met.
WRT W coming by and staying over, the goal here is to protect yourself emotionally so set the boundaries you need to set. Insisting on some family therapy to help you co-parent or MC to work on communication skills specifically wouldn't be an unreasonable request. If she does sleep over it should not be in your bed, IMO
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015