I can't explain this frustrating problem - no one can actually - researchers still don't know why exercise is so damaging for many FM and CFS patients, but I certainly share your frustration. The only thing I can suggest is to lead your daughter to credible sources that she will hopefully trust.
Check out this link from the National Fibromyalgia Association (http://www.fmaware.org/site/News2?page=NewsArticle&id=5271)
It goes over how to exercise with FM. Note that it does say exercise is good for FM patients but also notice how detailed the instructions and how careful you have to be to enjoy the benefits - this is not normal exercise! Its small amounts of very carefully managed exercise.
Whatever type of exercise you engage in you should be sure to be stretching as well -that's important for loosening up those contracted feeling muscles that so often occur in FM.
Good luck with your daughter - it's tough battling a chronic disease and one's family members at the same time.