Yeah good or bad children will copy their parents habits and values when it comes to food. You can often see this in a self service buffet environment the kids plates will often be a mirror image of their parent's plates even if they serve themselves.
In general most people don't get enough...
When you joined the bigger gym what were your honest expectations? Did some part of you expect that your gymnast would step into the bigger gym and just blow everyone away with her raw talent and with some polish she would fast track to elite?
I know this might sound counter intuitive but...
She sounds athletic but gymnastics might not be a good fit (at least at this time). She sounds like she wants to play and experiment not learn a discipline, if doing non-competitive rec classes are an option maybe just look into those and enjoy gymnastics as an activity.
The physical training tests are listed here: https://usagym.org/women/tops/, for my daughter the training consisted just doing those exact drills over and over and over again.
The coach also can just stand there and as long as they don't touch the athlete it won't be a deduction. Sometimes just knowing a coach could catch them is enough to help them through the mental block.
Very little good happens when parents try and coach routines.
I know you are trying to be helpful and let her "maximize" her training time, but the coaches already know what the deductions are and are choosing not to focus on those things. Gyms have different philosophies but most are...
6 is not too young to compete, you could ask if there is room on team for her, but it is right before the season starts and she wouldn't know the routines so most likely they would say no.
You said she joined this group mid way through the year, so presumably at the same point this next year...
Probably best to not draw attention to it, I know you want to help, but things like "how was your back walkover" or "did you try .... " after every practice will just make it worse.
Coaches have been through fears themselves and worked with other kids with fears, it will be ok. Might also be...
This is a sport that has a lot of bad news and/or sugar coated news that needs to be given and getting too close with families or families with each other has the potential to put them in some uncomfortable situations so creating social separation is way to kind of pad people from that.
While...
This is normal, if there is something you do need to do at home they will tell you, but don't expect to need to do anything just be a cheerleader for your gymnast. In general very little good happens when parents try to coach their child in gymnastics. If they want to do some body weight...
If that is the only reason that you'd do gymnastics than quit now, if the journey isn't part of the reward than you are setting them up for a lifetime of failure. Don't try anything you might love if you can't make it to the top! Don't do things for the love of it if you aren't the best! What...
Until meets start the interaction is on the low end, but at meets we sit with the other families and sometimes go out for meals together after awards. This kids that are friends outside of gym tend to have parents that also interact with each other more often.
Some families are very private...