The bottom line is you can tell them she's your child and you know what she needs. When you think about it...... the schools are in the business of helping kids enrich their lives, and the school officials should be able to understand that education is not the *only* way a child can grow into a complete adult.
The gymnastics experience your daughter hopes to have will give her a view of herself, her peers, and the adults around her that few children, or educators, can hope for. She'll experience travel and learn how to conduct herself responsibly in the absence of her parents, and get a sneak peek into her future as an adult while still enjoying herself as a child.
The thought of her taking an online science course is an interesting one, as is your position about it. Gymnastics provides her daily with a living lab experience in physics, and I would think she could easily learn more online in that subject than her peers in the classroom. She's likely to be more inclined toward independent study in biology, anatomy, and physiology because, just like gymnastics, they're all about how our bodies work...... well, except for the botanical side of biology, although I have seen some coaches approach a vegetative state from time to time.
Problem solving is a common, complimentary, link between education and higher level gymnastics, and as gymnastics is her passion she'll develop that skill to greater depths in the gym than she would in a classroom. This expanded ability will enhance her classroom activities and make her a better student. Who, in the field of education, wouldn't want that for a child, as that is the best step anybody can take to become a lifelong learner..... isn't that the real goal?
Another thought is there must be others like yourself who's children are working through the system to rearrange schedules to make training longer hours possible. I would find those people out, chat with them about their experiences with the school officials and how the schedule accommodations worked for their children. I know this can work from my experiences with kids I've coached who've succeeded in college and professional careers, and am left wondering if the experience enabled their success beyond what they may have otherwise realized.