This is such a good question. Many parents find themselves in the same delemma. To push or not to push. The first priority is to preserve your relationship with her. She is a young teen with the challenging teen years ahead. It’s more important that she feel she can talk to you than win another ribbon. But I don’t think it has to be an either/or.
I don’t think the issue is laziness. A lazy kid would not get this far. It may have more to do with thinking that if she isn’t sure she’ll be the best, she doesn’t want to try. Her self-esteem may be so tied up with winning that she can’t risk losing. By pulling back, she can always tell herself that she would have won if she had put in the effort. It’s a “face-saving” tactic.
It’s normal for kids to want to try out a number of activities before finding the one that grabs their heart and attention. Many a kid has started an instrument or dance or sport with great enthusiasm, only to drop it later for something else. What concerns me about your daughter, though, is that she isn’t pulling back at dance in favor of something else. That also suggests to me that self-esteem issues may be at work here.
You didn’t mention what your daughter’s coach or teacher thinks. Is her teacher frustrated, too? Do you think the teacher has the kids’ best interests at heart — not just winning? If so, perhaps a talk with the teacher will be helpful. Often a teacher or coach can inspire a kid when the parent can’t. If the teacher is too invested in “winning”, don’t go that route. You may be able to address the self-esteem issues on your own or it may be that you can think of another relative or older friend who can talk to your daughter about it.
If those aren’t options, then I suggest seeing a family therapist with your daughter. This is not because I think you aren’t being a good mother. Quite the contrary. I think it’s better for a therapist to help you and your daughter solve to problem together as a way to lay the foundation for other difficult talks as she moves through the teen years. I don’t think it is helpful for a counselor to become a more important sounding board than her mother.
I wish you well.