Sounds like she's trying to push some boundaries there.... seeing if she can get away with trying to control you, iykwim. Hence her first saying that she's not going, even though she would be clever enough to know that you've gone to a lot of effort to get her ready, and then when she realised she wasn't going to win that battle, she demands that her Dad take her to the party. She won that battle, so to speak, I guess.
I don't know whether or not you did the right thing in making her go to the party, that's for you to judge. If I were in that situation I probably would have given her the choice, "either you come to the party with me, or you stay at home stuck in your room all afternoon while your friends are playing and having a good time at the party." Then its in her hands, but ON THE PARENT'S TERMS NOT THE CHILD'S.

I'm an unrelenting parent though, lol my policy is, I'm the parent, so what I say goes, or it doesn't go at all. lol
I think with kids even if it doesn't really matter whether or not for eg. her Dad takes her to the party or you do, its important to not give into her demands or she may think that she can control you, and maybe won't have as much respect for you as an authority figure, iykwim?
I hope I've made some sense here. lol
Parenting really is the hardest job in the world, sounds like you're doing a great job.

DS - 4 yrs
M/C (10 wks) - Aug 2002
DD - 1.5 yrs
EDD - 31st Aug. '05
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