Read up on 'emotional triangles'. Eliminating them will make your life much easier. Well.. it's made my life much easier though it's hard to do at times especially when the two other points are the kids and their dad.
So ya got a nasty gram? Par for the course. Sad, sweet, sappy, angry, indignant, rejected, annoyed.. just cycles she runs through. Tomorrow it will be something else. Explaining your point of view never accomplishes anything. Validate and "Gotta go." She is still checking for an emotional connection from you with lil pokes and jabs. When you blow up, are 'there for her', make her a number one priority she knows you're still 'attached'. Any attention brings its own rewards.
You're doing good, George.
And even with the kids, try that handy dandy decision making guide..
If it seems right, do it. If it seems wrong, don't. If you waffle or can't decide, don't.
Mom at the birthday dinner? Eekk.. option 3 perhaps. It's okay for Daddy to have boundaries, too.