"We had some really bad ones"
I am responding to this comment, and not to the thread's question.
I've seen some bad skating parents too. They get all too wrapped up in their child's skating. I guess it's because they have nothing better to do during the hour long skating lessons. They are watching their kid, and the other kids. And, they are all comparing and wondering if the kid is doing enough. Top the parent's insecurities with the fact that skating is very hard. Skills are not mastered in a week or a month. Rather, it takes several months to a year or so to just "kind of" do it. These parents have no clue as to how hard figure skating is. When their child doens't seem to be progressing, they let it be known. All a kid wants to do is to please the parent. Shot down. Add to that that coaches are tough and have to criticize for their job. . . and you get a burnt out kid with no self esteem.
So, my advice is to be interested and supportive of your child's skating. As an adult, I can take just one or two of my coach's many pionters to work on. So, don't overload the child. Just a few things that the coach wants improved. Understand what the child is learning. See Youtube, skating books, etc. Buy some skates for yourself. Skating will not kill you, and in fact, it will stregthen your appreciation for what your daughter is learning. And remember, leave the coaching to the coach. You job is to rebuild your child. Tell her what she did right and what looked better/more beautiful.