I would suggest asking her to leave immediately and do so in a kind and detached manner.
If she won't leave, I would take proactive daily notes on the interactions and record them, if you can do so without her legal consent.
Your best bet is detach, stay away, focus on you - GAL. Be the man and put yourself in a position where you can walk away with dignity and respect. You can't change someone else's feelings and even trying to show love at this point will come off as manipulative. Just let her do her thing and smile like the man you are.
I'm not sure why you would want to work on it with a cheater who openly wants out of the relationship. I personally would find that situation extremely draining and toxic. In fact, I know firsthand from my own experience.
We went to one MC session and the counselor validated all the negative garbage and lies my wife was spouting and basically told her to leave me. I was the guy who wanted to "fix" the marriage. I was the one who scheduled it and saw the counselor for IC for 2 weeks prior. I was the guy looking to do better for the relationship. Doesn't matter in the end, if they're already emotionally committed to leaving/cheating.
IC/MC won't always recommend saving a marriage, if they are presented a picture of abuse. Even if it's not factually accurate or skewed by an affair or whatever.
I'd suggest you find another counselor for yourself and just focus on GAL and your own health and wellness.
