What I meant was that if you can't work something out with this coach then you should be able to find another one.
As for having multiple coaches, some I have known would absolutely refuse to be involved, others are quite happy to share students. My personal view is that you're the client and you choose who to employ, but the etiquette seems to be that you need to ask first. One of many reasons why I am glad I no longer have lessons on ice, do patch or indeed have anything to do with rink politics. I don't know or speak to anyone at the rink I skate at now.