As a piano teacher, I personally wouldn't mind, but would probably think this mother isn't very "dai tai". Why would you want to see the cert? That means you are suspecting the teacher is lying about her credentials?
I think you COULD, but it's not very "polite" and "respectable" to do so. If you don't trust the credentials, then why even try?
A qualified, and experienced teacher would not need you to ask for such proof. You can tell from their way and style of teaching, and manner, and knowledge. Isn't that more "proof" than a "cert?"
I don't know, that's MY opinion.
As a MOTHER, I never question the credentials of my kids' teachers, I "test" them.... better than a cert. Teachers who have lots of certs... so what? It doesn't mean they know how to "teach" effectively.
Certs are a thing of "asian" culture based... they are of certain degree important, but I think Asia, esp HK parents are very narrow minded in this thinking, that CERTS mean everything.
Certs are EASY to get, just join a course, or a seminar, or a so called competition/festival/workshop, or part time course.... or even PAY for one....
However, knowledge, wisdom, the ability to teach what one knows, and have experienced..... these are what's important, and what's priceless.