She is a tough one, isn't she? Sounds like how my W was a couple years ago.
Don't roll over. Try to negotiate in good faith, like you said you would. Ignore her jab about you again causing a problem.
How about:
"We seem to be stuck. I'd hope we can work this out in a way that's acceptable to both of us. I sent you a message on May 27 telling you about my plans for the end of June. Since I didn't hear back from you, I assumed it was okay, so I made reservations and finalized my schedule at work. I had no idea you wanted to take the kids at the end of June. It would be very difficult for me to change my plans now just two weeks away. If I can keep my plans for the end of June, I'd be happy to let you have the kids at the end of July. That way, we each get something we wanted. Can we compromise on this?"