Honestly, I don't see anything wrong with what she said, if your daughter is not trying her best, or copping an attitude. It's easy for kids to not give the whole story and try to get you on their side and play on your sympathy. I would talk to the instructor first, be reasonable and open to what she has to say rather than going in there guns a-blazin', ready to rip her a new one. And realize that maybe your daughter really doesn't want to do dance any longer, but feels she has no choice because you keep insisting on it, pushing her, and maybe even reminding her of the money and time you have spent so far. It doesn't matter how much money and time you guys have put into it - if she is done, she's done.
For a little perspective: I did marching band in high school. A friend of mine in band had parents that were very competitive and were always pushing her and pressuring her to be the best - she had to be first chair, she had to get top ratings at competitions, etc. Looking back, she realizes how stupid it all was. All that pressure - for what? It's not like we were preparing for a career in music! Neither one of us has picked up our clarinets since we graduated! It's not that we didn't enjoy it, but the point is that this was something meant to be enjoyed, to be done for fun, not be one more thing to stress out over. It just so happens we both work in the same vet practice now (I am a vet, she's a tech) and while we didn't become professional musicians, it wasn't a complete waste of time either. We got out of it what we got out of it (memories, friendships, a sense of achievement) and moved on.
A friend of ours has had her daughters in competitive gymnastics for years as kids - 20 hours a week in the gym, tournaments on weekends, the whole 9 yards. When the oldest hit middle school and decided she didn't want to do it any longer, that was it. Mom always said she never expected them to keep going if their heart wasn't in it. She doesn't consider it a waste of time or money that her daughter decided to stop. The younger daughter is still into it, the older one decided she wanted to do other things - she's been on her basketball and volleyball teams in high school and has enjoyed it immensely. The gymnastics gave her a good foundation for everything in her life (hard work, athleticism, etc.) but she was also getting burnt out. So maybe, what you should be doing to talking to your daughter more, and honestly trying to listen to her and what her feelings might be, and consider that she might be done with dance - at least for now. Maybe she just needs a break, maybe she wants to try something else, or somewhere else. She's only 11 for crying out loud - unless she totally loves competitive dance, is planning to do dance as a career or whatever, you have to ask yourself, what's really the point if she is not having fun?