The sort of behavior you describe is not unusual in a child her age. Every child develops different skills at different times. Kids like your daughter often develop some skills earlier than usual and others later. It seems she is above her years in coordination and intelligence. But self control can be slow to develop, lots of kids at 6 or 7 still have very, very limited amounts of self control. Concepts of fairness and consequences are hard to understand at this age, you are not doing anything wrong as a parent. She is simply not ready to understand all of these concepts.
Kids her age live in the moment, they do what feels right at the time, they aren't yet capable of delayed gratification. They can't think "OK well I'll work hard now, and I'll see the results in a few months", or "I'll behave now, because I will have consequences later".
Her intelligence may also be an issue. many very highly intelligent kids are mistaken as having ADHD, these are the signs of a high intelligent child and you'll find a big crossover between these signs and ADHD symptoms.
1. Very high energy levels
2. Require less sleep than other kids her age
3. An almost adult sense of humour well beyond her years
4. Picks up on concepts very quickly almost like she always knew them
5. language very developed for age
6. Motor milestones ahead of her age
7. Needs constant stimulation to keep her interest, the brain needs more stimulation than the average child.
Highly intelligent kids are very active, especially at her age. They get bored quickly and will be disruptive. Many have never had to try in their life to do anything and pick things up so quickly that they don't really understand what it means to actually try. They will just play up if they have to put any effort in, because they are used to just getting it straight away.
It also seems interesting that your childs coach ignores bad behaviour and hopes it will just go away, but your daughter will keep at it until she can't be ignored. It means your daughter loves attention of course as do many girls her age, but she keeps trying to get it by doing the wrong thing. This often means that it is too difficult to earn attention from doing the right thing. Think about it from her point of view. If a child is well behaved, it might be recognized and it might not, often it is not rewarded until say the end of the week or after a long time of good behavior. While bad behavior can almost guarantee immediate attention, or attention if she pushes it far enough. Does this coach give as much praise and attention for good behavior?
If you are unhappy with gym consequences, give your own. If she misbehaves at gym then its home to bed early with no treats or television, its likely she will test you a bit if you put such consequences in place but stand firm and she will soon get the idea.