The problem with you suggesting fixes to her is that it can make the learning process even longer. Every coach has their own way of teaching, and fixing skills, when parents try to verbally coach from home it can really cause huge problems. Can you imagine when your little one goes to gym and tries out what you tell her, the coach says "what are you doing that for?", dd says "my mom told me to do it like this.". The coach is just not going to be happy, even if you just want to help.
I totally get the urge to "help", but in the long run it may make it harder to learn the skill if you keep giving her tips.
There are so many skills in gymnastics that trip a gymmie up along the way. The first big, important one is really the kip. Before that the most important thing is that your dd learns strong basic skills, trusts her coach and is able to know that gym is her sport and not mom's sport. This may seem harsh, but having been here for a long time I have seen what parents coaching can do to kids. I know you mean well, but seriously letting her have fun right now will be way more productive than giving her tips in the long run.
This isn't personal, or about you, it is just about coaching.