G.B.
Here's the thing. Dance lessons teach the child "how" to use their muscles and how to place their feet, etc....if she's getting hurt while dancing at home chances are she is damaging her bones and tendons.
Google what dance does for kids bodies and you'll see what she's doing to her body. I suggest you either discourage her from doing stuff this strenuous or that you sign her up for dance lessons and let something else go. If she really loves dance this much she needs it. Dance can take her to college and on to a career as a dance teacher, a performer, an actress, etc....it is a very lucrative career and if she loves dance putting her off will only make it harder on her when she finally gets to take classes.