I agree that you are not being grumpy, but I do think you are catastrophising a bit. Your hairdresser knows the arrangement, and should have no problem in complying with your wishes. So what's the worst that can happen? The salon loses out on ten minutes or so of useful time? Well, in that case it is on them to sort out the situation, as it was caused by their receptionist's poor English. If it matters to them, they will.
It is frustrating to have conversations that go nowhere because of language difficulties, and IMO it is up to employers to ensure that these frustrations are kept to a minimum. It's not being intolerant to expect that a receptionist (or call centre worker, or any customer-facing employee) can communicate effectively. It's nobody's fault, but it doesn't make sense to put someone who has problems communicating in English to be a front-line member of staff.
I think you should be kind to yourself, and maybe have a chat with your hairdresser about it when you see her.