I don't know... The root of this conflict is lack of communication. I think you need to back off of this fight or she is just going to conclude that you are being stubborn and selfish. Even though YOU ARE NOT (don't think I'm name-calling here.)
I really would back off from this and reconfigure the trip for a shorter period of time. She does have a right to an opinion on this matter. I wouldn't want to be apart from my son for that long, either.
I know you are angry, and rightfully so, but I don't think staying firm on what you want for this vacation is going to yield good results. It would be different if you had discussed this with her prior, without making assumptions about what she was planning based on heresay.
This advice probably isn't what you want to hear, but it is what I think will make you the better man in this conflict.
Perhaps others will chime in with differing perspectives.
