You need to take care of YOU now. If that means a separation for you to get your head on straight, then do it. That therapist was WAY out of line to "beg"you to do anything!!
The best thing that can come of the therapy your MIL wants to be involved in is that the therapist will recognize immediately that she's a big part of the problem and will call her on it. Unfortunately, that will probably mean the end of her sessions!!
Enjoy your peace and quiet.