You were not "snippy" at all. With this more complete info, it sounds to me like your W really does need to be reminded she is a mom. That is where counseling may help. If a side benefit is waking up to reality of your stitch, so much the better.
Your previous posts were written more about you - I read that you were hoping that the counseling would be more MC and not child-focused. My bad.
But do steel yourself. As long as the OM is in the picture your W is in denial and will be about your daughter as well I fear. She may get very defensive. Sometimes they agree to counseling only to validate their "nothing is wrong, I am right, no one is being hurt" position in their own minds. Plus, she wants to show she is a great mom in case of custody issues.