One problem is that your actions/words say, "I have a say in what you do or don't do", as though you are still married. She basically asked if you'd watch the kids an extra day and you get up in arms that she is cancelling something with you as though you are dating. If one of your buddies cancelled plans would you get all up in arms about it? Face it, you are divorced, and you lost any right to expect these things. Watch the kids because you want to or not if you already made plans of your own.
Quote: But as long as it isn't a date.
I think she's trying to tell you that she doesn't intend to end up with you again. My XW did that a lot. She was willing to do stuff with me as long as it didn't lead me on. Frank, you might have to accept that she just wants to be friends and it might never be anything more. Are you okay with that? I don't know if that is the truth, but I think you are better off assuming that you will never be a couple again and act accordingly.
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