Not sure how to interpret any of your wife's actions considering she's with someone else, which I guess I'd interpret to mean she doesn't want to be with you. So, I'd focus on coparenting and on my own life. If she wants to handle the kid stuff in a friendly manner, then that's good, but I wouldn't take it to mean anything more than that. I've been divorced for 8 years and my ex-wife still does stuff like you describe. I doubt it means she wants to try again with me since I'm remarried. So keep the session completely focused on what is best for your daughter and who cares if some of it makes your wife uncomfortable with her parenting skills.
Me
In the end, it's not the years in your life that count. It's the life in your years. Abraham Lincoln
It is hard to fail, but it is worse never to have tried to succeed. Theodore Roosevelt
