hm...sorry that you didn't get a response right away, but I am sure that many of us are dealing with our own holiday "stuff."
That being said, can you just copy and paste what you wrote in this post to your ex? It may not do any good, or it may open up some communication between your D and her father... assuming that she has tried to talk to him about it with him already and he has been too hasty to dismiss it....
Ultimately, at her age, she is old enough to make her choice. Let her know that. Tell her it goes both ways, too - there may be a time in the future when she chooses to spend time with him rather than you for some reason. As much as it hurts to watch, their relationship is ultimately their relationship, in the end. The best you can do is be her sounding board and get her outside help to deal with the anxiety (he might not hear it from you, but would most likely if approached by a counselor for his daughter...).
What a terrible position that WAS's put our children in...I often look at my kids and realize that I am the lucky one, having finally removed myself completely from his choices - they will always have him as a father, for better or worse.