Many years ago, I knew a couple headed for divorce. She wouldn't go to MC because there was "no point." So the H's IC suggested calling it "divorce counseling" instead, and she went along. (As it happened, they had some pretty basic communication problems and they ended up staying together, but that's not my point.)
If you think of it as "divorce counseling" then you can focus on how to minimize the impact of the D on your girls. Sort of like mediation, but focused on the relationships rather than the assets.
This may be your W's motivation. Or, she may also want a place to rip into you, with the "referee" in her corner, just to piss you off and make you want the D. Or, she may have realized (or her lawyer suggested) that it "looks better" if she agrees to MC.
In any case, you don't want to be the one refusing to go to MC, especially after one visit. If they really gang up on you and you can't stand it, then suggest that she pick a new "neutral" MC, and if she refuses, then at least you're on an equal footing. That is, you can't agree on a counselor, rather than you just refusing to see hers.
BTW, I went through this. We were going to MC for a year, then the counselor (over 70) was diagnosed with cancer and died in a few weeks. We both found IC's, and eventually we tried MC with her IC. This counselor insisted on having one solo session with me before starting MC, to get my side of the story. Even so, it was clear that they had an agenda and although I was willing to continue, my XW declared it "pointless" after two sessions.
