Let me give you some advice...b/c I dealt with and continue to deal with a ranther simaler situation. *sigh* It's gotten rediculous and I may sound a little callous, but please let me save you the headache!
I think when you meet with the parents and the girl you should first let her know that you are aware that she is afraid to fly and that of course you will do whatever you can make her feel more comfortable...BUT as she is (I am assuming) 14 years old, she is old enough to make a choice. If she feels that flying is going to be too difficult she should not come on the trip. I say this, b/c the more attention you give to this fear the more hysterical she will be about it. This is a trip to Disney, not a forced march to a wilderness camp. This is YOUR vacation that you are very generously including her in. This is a not a trip about her fear of flying and babying and cajoling her along. If she wants to come, GREAT! That means that she is assuming the responsibility to handle herself in the most appropriate way she can. If that means she needs a couple of xanax to get there, then she should do it. I'm going to assume once again that this is a fear her parents have probably enabled without meaning to. Don't join that bandwagon. Be kind but no nonsense about it. If she wants to come then she needs to be prepared to fly and deal with it the best she can. If she thinks that doing so won't be possible without some sort of a hsyterical, attention seeking meltdown, then she needs to stay home.
Maybe it was partly how I was raised, but if a family had extended such a wonderful invitation I wouldn't DARE have complained. I would either suck it up and deal with it or I would have said no thank you. But I certainly wouldn't have asked them to inconveniece themselves and make the trip over about me and my issues. It's RUDE! It is NOT your family's job to take on a major "issue" on your vacation...especially when she is not your child. This is vacation, not therapy!
hope this helps!