I make a point to invite the W to all events and activities with our daughters. I also make a point to invite myself to any activities she does with them, if she doesn't explicitly invite me. There's nothing wrong with inviting her along; it's not pursuing. If anything, you can show her how good a father you are, which is very attractive.
I wouldn't worry about her saying "no matter how this ends up" when going to MC. She's just scared.
