You should really take this up with her doctor. Children's bones and muscles aren't generally developed enough to do this kind of activity. Parents that "encourage" their children to weight train etc often end up doing irreversible damage.
I have to mirror some of what has been said here though. As a mother of 3 and very active in my kids schools, I can't imagine a child who "wants" to run so much. My kids are passionate about music and still getting them to practise is a chore. It does sound as if YOU want her to be on the team or she feels that you would be more interested in her IF she says that this is what she wants.
Take it down a peg. Talk to your daughter about why she wants to be on the team and you may find out that she feels that that is what is expected of her. Talk to your doctor and her gym teacher and get advice there.
best wishes.
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