When you coach them from home (and any teaching them or corrections really is coaching) it interferes with the relationship between coach/athlete and causes confusion for the child as to who to listen to "Do I do what my mom told me or my coach?" And often at the compulsory level, some gyms don't always worry about fitting exactly into the compulsory mold. If the coaches aren't concerned with it and you trust their philosphy and coaching, then let it go. Because sitting with her and telling her to change her run into tumbling passes IS coaching.
If it concerns you that much, I would email the coaches and let THEM decide how to best deal with it.
But again, I do consult the coaches and if like her bar coach told me that he wishes she would get her arms straighter on her kips and free hip, I do let them know that I will discuss it with her and have her work at open gyms. The run thing, I showed her on her video where and when she took the extra steps and had her walk through the pass minus the tumbles at home. I will listen to Dunno when he said NOT to contact her coaches. He hasn't straid me wrong in the past. Honestly, what is so incredibly wrong?
I am such a realist. I do not let gymnastics govern my life nor my child's. But I do let it aid in helping her develop into a mature and responsible, for now little, being. In my book, everything IS a learning experience. Most times in the past, I had a direct patch to her coaches because as a five year old she did many things a five year old does. She told many a story when she started with them. In other words they caught her lying a lot! They consulted me to help. She was a "meanie" to some girls. They consulted me to help with the situation, and I did of course.
I have never stepped outside of the line and "coached" her as I saw fit. Like a teacher, I expect my child to learn her gymnastics from her coaches. They have appreciated how I handle things with her. I think I heard before on here..."We are expected as parents to help them with school HW" I know I expect to have primary students get that help from parents when there is a difficulty especially. I don't take that to mean that I introduce a new curriculum. I simply reinforce what her coaches have been trying to make her see/get all along. Children do benefit from hearing the same thing in different ways. Dang, RTI has permeated my mindset in all things!! What has teaching done to me?!!!! I really do love my job!! No seriously, I do!!