Admittedly, I don't know much about competitive gymnastics and cheering, but I believe I am sensible enough to understand that two such demanding competitions on the same day would be too taxing for almost anyone.
After all, both involve warm-ups and stretching, etc. And then there's the drive, which sounds like it could be stressful and hectic. Then there's the timing. These types of events can often experience delays (equipment issues, injury to a competitor requiring immediate attention of medical personnel and a "time-out" from the competition to allow for emergency care, or any one of a number of problems that can arise). And, both are physically demanding. That's a lot for a young body to be pushed to in the space of a few hours.
Since your daughter is now in high school, this really should be something that she brings up with her coaches. It's time to learn that skill. Sure, have her send an email if that's more comfortable.
I believe that part of devoting oneself to anything (a sport, a skill, theater, vocal performances, playing an instrument) is recognizing one's limits. Also it's important, when committing to performing or competing, to appreciate that some things just won't be possible.
That young talented gymnast who won the gold medal at the last Olympics (I forget her name, Laurie maybe?) was on Dancing With The Stars last season. She revealed in interviews and talks with her professional partner how hard it had been to devote herself entirely to gymnastics. She didn't regret it, but she said how she had never been on a date, didn't go to any proms or school dances, and hadn't gone out to movies and things with her friends because every waking hour was spent at the gym. The lesson she learned was that she could do one thing well, but not everything else.
Now, the person who just wants to play the piano for her own enjoyment, or the person who just wants to work out at a gym, or who likes to take tap dancing classes for fun can do all the other things - the vacations, the school activities, outings with friends, etc.
It sounds like your daughter needs to evaluate her devotion to both sports and decide whether she wants to just participate in both, or excel at one. And help her figure out which one she enjoys, which she could possibly get scholarships for or continue in college, and which one she sees herself in.