Obviously lot's to think about. Right out of the gate she's not being honest. Her being surprised you still want be married is manipulation to shift blame. After 3 letters she knows where you stand.
You're kind of in a tough spot right now. I will give you my opinion based on how I see this playing out.
If she really wanted to work on the marriage you would attend MC while living together.
If you don't agree to this she most likely files for divorce.
If you do she most likely cake eats while she gets her ducks in a row a says "we tried".
The DB alpha move would be to tell her that you understand that she feels you need to separate but you are not leaving your kids and the house. If she wants to move out you will not stand in her way. You would like to remain living together and work collaboratively with MC to fix your marriage.
From what I know about you U your mind is going to be spinning based on her statement " I'm surprised you still want to be married". All part of her master plan.
Think about you as being the captain of the Titanic and you just hit the iceberg. You going to try to get a seat on the life boat or are you going to dig your heals in and go down with your ship.