I would suggest putting it aside to ask MC to assist in how to find a solution to the issue. Isn't that what you were seeking when you chose the C?
I think the two of you need to spend time without the kids, but not for the purpose of hashing out your problems. Try to have the mindset of beginning a new relationship when you have these first few times together. It should be with a light & fun attitude. If she mentions something that has been an issue, just say something like, "Let's be sure to bring this up at the next MC session and see how to resolve it. Let's just enjoy spending time together right now.". Of course, say it in your own words.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!