I don't know of any gyms around here that close for that long. Our gym closes for two weeks over Christmas break for all the rec classes, but the team still comes in to practice. It's modified and they usually get a few days off over Christmas and New years, but since it's right before season starts, there's no way they'd get two weeks, or even one week off then.
They do give the team a break (with no gym closure, though) usually last week of May/1st of June over Memorial Day weekend, then the team moves to morning work outs for summer.
This year they will get another week off over the 4th of July due to the holiday and the fact that most of our team coaches will be heading to Cali for National Congress.
My kids swim, swim, swim. We see movies, go bowling, go to the aquarium, ice skate, etc. Sometimes we head to San Diego and stay at the beach. It's too hot out here in the desert to do anything outside in the summer unless you are swimming. They have no interest in going to a gymnastics camp.
They need the physical and mental break. It makes them eager to get back into the gym after that week off.