Mozza-- just catching up on your sitch. I think in the end your response was fair. But I just wanted to tell you that my parenting agreement with my H specifically states that our D will get to see both of us on her birthday.
Be mindful of when things you consider "truth darts" involve the kids. Your guiding principle should always be "what is best for them? "
It doesn't necessarily mean that you should change your plans this year, but it could be something to think about for the future.
Can D6 have a special Skype session with her mom on her bday? Does your W know where you will be if she wants to send a special gift (birthday bouquet for ex.)?
You've got a lot of anger that seems to be clouding your responses (in your mind, at least, even if it doesn't come out in your email). Try to let some of that go, for your kid's sake. ..