She is ONLY 4 years old. 4 year olds often don't listen, especially when they have to wait for their turn, etc. She is acting her age, that is all. At age 4, gymnastics should be FUN, FUN, FUN.
How many hours a week does she do?
If she is pre-team, maybe she needs a decrease in hours. If she is talented, taking a break or decreasing hours is NOT going to hurt her. My DD isn't super talented and she didn't do "pre-team" type class until she was 5 and that was a very low pressure, fun, 1.5 hour class 2 times a week. Even at that age she sometimes didn't listen.

Heck, she is 6 and a level 4 now and sometimes doesn't listen. LOL.
I wouldn't do privates. That isn't going to help her learn to pay attention. As she grows older, she will pay more attention. Let her be what she is, a little kid. If the coach has issues with it, then maybe she just isn't ready for pre-team yet. Let her do rec, have fun and not be stressed.
