I've said in the past that if you think you need a coaching change you should research it a bit, and talk to people about who and how. But that advice was too broad, and a recent situation leads me to a more subtle recommendation.
As ever, if you are unhappy with your coach, for whatever reason--tardiness, scheduling issues, skater progress, et cetera-- always talk to the coach first. Remember to not be accusatory, and always to frame statements as they affect you or your skater, and not in terms of faulting anyone. (Lots of resources on the web about active listening and non-confrontational conflict resolution.) Then you need to listen to what the coach says; for instance, if the coach says the skater isn't on the ice enough to achieve his or her goals, this is probably a giant clue as to the source of your skater's lack of progress.
If you can't go to the coach, through either legitimate concerns or cowardice, then there are two people you cannot talk to. Do not go to another member of the coaching staff. First, it puts them in a very sketchy ethical position; they are obligated by the PSA to report to the current coach that they have had this conversation. Second, it damages your coach's reputation, which I'm going to assume you do not want to do.
Do not go to the parent of someone with a different coach. First, this drops you into the gossip mill, and second, it exposes that coach to an ethical violation as well, possibly without the coach even being aware of it. I'm a bit on the fence about whether you should talk to other parents with the current coach; again, this can have the effect of damaging that coach's reputation and livelihood.
So I've just taken away all your resources, haven't I. But there are people you can talk to.
The current coach
Most coaching issues are about communication-- both not talking and not listening. State the problem as succinctly as you can. "I am concerned about the schedule, our lessons don't seem to be a consistent length" (translation: I feel like you're always late, or talking to someone other than my skater during lessons); "I am concerned about my skater's lack of progress" (translation: I have not been following the coach's advice about how much she should be skating.) Then LISTEN to what the coach says. Sometimes just putting a concern in front of the person who can do something about it is all it takes.
The Skating Director
You don't have to have some giant criminal issue with the coach in order to go to the skating school director for advice. I've got a skating director who is notorious for staying behind the scenes, but is absolutely available for parents who want advice, as is every director I've ever worked for. Most facilities bar the skating school director from having private students at their facility, so they are about as neutral a source as you're going to get in your own house. Again, make sure you frame your concerns based on reality. If you ask her to keep it confidential, she will.
USFS Parents Committee/ISI
This is a wonderful resource that is underused by recreational skaters. They pretty much exist for this purpose. Call them up, explain the problem; they will connect you with someone who can help. I don't know if there is a direct counterpart at ISI, but if you call their membership office, I'm betting they will have someone you can talk to. USFS Parents Committee has a Facebook page (of course they do) with emails (under Info) of all committee members.
A former skating parent
Talk to someone who's done with the program. Better yet, someone who's done with a different skating school. Again, your skating director is a good resource for this, and will be able to steer you to someone receptive.
Icemom has an "advisory committee" that she taps for difficult skating problems. Check out "Ask the Icemoms" on her site. The panel consists of people like former champion skaters, current coaches, and skating moms, including one mother of an Olympic skater.