Gymnastics is such an evolution....for the child AND parent. When my kids were young, helping with handstands, and mushroom circles and walkovers seem so innocent. For the most part it was but after years of innocent, sneaky coaching, I find it has actually taken a lot of the 'fun' out of walking on their hands at home, or messing around in the front yard with friends.
I am guilty of helping myDD remember her routines, so yes I am a hypocrite, like most parents of gymnasts. (Remember, we all know NOTHING about gymnastics right?)
I think more than anything, it violates the safety zone gymnasts feel when they are home with their parents . When they come home the last thing they want to think about is gymnastics. No matter how qualified you are, it will take its toll on your relationship. Parents who coach their kids IN THE GYM may have a better system because they leave the gym, and there is no more gymnastics....
If your DD needs some harmless help, I am sure you will do it regardless.....just ask the coaches so that at least you can actually be complementary. If they ask NOT to teach something, then don't.
As far as home equipment , even what you have, it is ALL useless past L4. The only thing that still gets the occasional use is my floor beam....my cats use it as a scratching post and if I take it away the couch is the next best thing.