Tinkerbell, the niece needs to know that the decision whether to go or not is in HER DAD'S hands and not yours.
Did you ever have the conversation that many (including me!) with her that let her know that it was Dad who said "No" and not you? I still think that's very important, because Dad sounds like the kind of person who wants others to be the bad guy (just from what's been presented here - some passive/aggressive stuff going on here).
Barb D, with all due respect, I disagree. I think having a conversation with the niece and the uncle in the same room with others around, done in a non-confrontational or blaming manner, is an ADULT thing to do. Who cares if he gets mad? If he does, then some warning bells would certainly go off in my head! I really dislike walking on eggshells around people just because I'm afraid they MIGHT get mad at normal adult conversation!
If your uncle's decision is a rational one, he can calmly say to his daughter, "Yes, as your dad, you aren't going because (insert reason here)".
Oh, and whether she has the chicken pox or not (and if this is a different reason why she can't go) - she STILL needs to know that Dad, and not YOU, made the previous decsion about her going!