Hi Adelmaal
I've got the same problem with my ex, in that he's not willing to compromise anything, the rules are his and that's the way he wants to play it. The difference is, I did have a lawyer and made sure I got all major holidays with my son.
When it comes to changing "our days" I'm learning that it's best to put it in writing what you want. You need to document everything you are doing to show, one day, that you have tried to reason with this man and have tried to make your daughters needs first. She's at an age now where she can speak up, and if she wants to do Christmas with you, he needs to take that into consideration. That being said, I know what you are up against.
With my ex, I approach it in a calm almost casual manner "hey, we're doing this & that this year in December, and I would like to know if you're willing to switch a date with me? I want December 25, and since I have ____ during the Memorial, I thought that would be the best switch for us" or something like that. Usually, when I make it come out "his" idea (in his own one celled brain) he is usually receptive to it. Tell him you need to know by a certain date & get it in writing, get it signed by both of you and get it notarized. I have to do this each & every time. I can tell you mediation is in our future as well and no doubt he won't go or won't agree to anything. That is not in the best interest of the kid and the courts don't like that! Just a thought!
SK