It is not uncommon for some gyms to have an "elite track" program which requires two workouts/day. The families that choose this for their daughters often decide that home school is the best option for their gymnast. Not every gymnast is a good fit for this program. Not only does it require certain skills, but it also requires other traits from the gymnast like work ethic, mental toughness, coachability, attitude, AND it also requires total commitment of not only the gymnast, but their family. I personally think it is wonderful that the gym is helping to facilitate the often overwhelming and confusing process of homeschooling. It makes perfect sense to me that this would be by invitation only. I am sure the tutoring staff or whoever they bring in for educational assistance and proctoring is limited and they need to make the best use of their resources. Sort of like a return on investment. I would be willing to bet that the participating gymnasts don't "get" extra practices- but rather I am sure the extra practices are required and part of the curriculum.
Is it fair? I think so. Not every family is able to make the sacrifices needed to go far in this sport. When you find one, and it contains a gymnast with talent and potential- I think it is absolutely fair for a gym to be selective in their process.
In any event, it sounds like you are happy with your children's current education situation.