D..
I think that perhaps you should ask her if she is willing to watch her 6 year old sibling after she finishes performing. When she has a fit, then ask her how she would feel if you were having a "fit" over having to bring her to her dance performance. Ask her if she loves her sibling. When she says she does, ask her why she would say that you don't love her for not staying after her performance.
When it comes down to it, she wants what she wants (to be a queen for a day) and she doesn't care if she makes sense or not. You do what you originally planned to do. Tell her what's what after this conversation and don't talk about it anymore. If she persists, tell her that she had better stop arguing with you or you won't be available to take her to her dance performance in the beginning.
She needs to learn her place. You need to gently but firmly show her what that place is.
Dawn