First of all, they're all cute. So damn cute. I love the kids; I think in 10 years of teaching I've met maybe 3 or 4 kids that I just didn't like. And I always feel really guilty when I don't like a child. What kind of horrible person doesn't like a child? (And what kind of doomed child is unlikable at the age of 5.)
The dilemma for the coach then is making sure you do your job and not the parents' job. It is the parents' job to tell the child that she is the greatest thing since sliced bread and that everything she does is wonderful (to a point). It is the coach's job to separate her personal affection or enjoyment of the child and the child's ability to perform the skill at a passing standard. Passing a child because you like her and don't want to disappoint her (or her parents), or because you think she'll get it eventually, is not doing anyone any favors.
I always tell my students that I want them to feel successful on the first day of class, not the last day of class. If they can handle the skills on the first day of class, then success on the last day of class is guaranteed.
So what do you do if your child is passed too soon?
It's actually easy. Do nothing. Watch your kid. It's possible that she has not noticed that she's not as advanced as the other kids. The coach however will notice, and a good and compassionate coach will take that into account and give your child remedial skills to work on that will bring her up to the level of the class, without the child feeling punished or singled out.
If you're really concerned about it, talk to the coach. Some solutions are to just bring the child skating on her own (you should be doing this anyway). If you can't skate, find a babysitter who can -- ice rinks are full of reliable teenagers. Doesn't have to be a lesson, just babysitting on the ice, at babysitting cost. You could try signing your son or daughter up for a second class at either the old level, or the new one. You could do a couple of private lessons.
Up through the lowest freestyle lessons, "cuting up" is annoying but not a disaster. Kids really do figure it out and catch up, although some kids will never acquire the technical expertise they've missed (things like toe pushes, and poorly executed turns). It's a big problem after Freestyle 2 (half jumps, beginning spins) because the subsequent skills are complex and dangerous if your technique is poor, plus it's very hard to unlearn bad jump technique.
In the freestyle levels, get a private coach. Do NOT hire the coach that cuted your child up, even if they say they did it because "she's so talented, she'll get it" or "I didn't want to hold her back, she'll be bored." That is a great big giant red flag that a coach is more interested in your $35 dollars for private lessons than in your child's well-being.
And just to be clear, yes, your child is cute.