The schools around here used to exempt varsity athletes during their season, but they've all gone back to everyone taking the required gym class. It was starting to open a huge can of worms. Gymnasts, dancers and swimmers were asking for exemptions because they were working out with their club teams. Kids who hiked with their parents or did an exercise video at home would even ask for an exemption.
I personally don't see what the big deal is with your daughter taking gym class. She sounds like an overachiever with a tough class load and schedule. Maybe learning a new sport and "playing" is good fun relaxation. Plus I don't think confining yourself to one sport is healthy. Fitness continues long after sports and I've seen so many superb athletes have no clue what to do to stay in shape when they've finished competing.
And please don't say your worried about her getting hurt. I'm not saying your being one of "those" parents, but I see parents all the time who won't let their kids do anything physical unless they're supervised by their coaches. Most kids aren't going to the olympics or getting full athletic scholarships and don't need to be treated like eggs.