I think kcab is absolutely right that having a coach present accelerates progress. Unfortunately, that's not how the music world operates. The best one can do is to have frequent lessons, and find a teacher who really teaches the child HOW to practice.
I have to say, however, that having an involved parent is NOT the same as having a coach (unless, perhaps, the parent is a musician herself). I can see kcab's point about not wanting the child to censor his or her feelings of frustration, but I do think that it's different for kids than for adults. My guess is that for most kids the "censorship" that keeps them from having a meltdown in front of a teacher is probably very helpful in creating the calm mindset required to work through a difficult problem, and therefore very conducive to making progress. This is premised, of course, on having a teacher with whom your child has a good "fit."
