V, I think you are really reacting to her stuff. I guess these are the issues that need to be addressed between you.
About the awkward moments, can you say," I am not sure if it is a good idea" - then they can ask her if it is ok to ask you to stay. Kids are not dumb and they know that neither of you wants to be the bad guy and it sounds like they don't want to judge.
You could be the better one and ask your W about these situations and her input. Me, with my exh, I recognized that the kids felt awkward at times and jumped in to make things ok when possible - but then I made all the decisions in my previous M and had to be the mature one.
You have to KNOW that you are not the bad guy! Your M is the issue and it affects the family, but it takes two and you know this so stop taking all the blame.
