Could anyone help me with can vs could in a request? I know 'can' is used in an informal way 'Hi bro, can I use your pen?' and 'could' in a formal way 'Excuse me, could I use your pen please?' But when a mother asks her son to turn down the music, it is an informal setting but 'can' doesn't seem right and 'could' does 'Could you turn down the music, I'm on the phone.' Thank you in advance. I couldn't find this specific request in previous tags.
Could is considered more polite than can when making a request. But IMO, in most cases, the politeness of the request has more to do with tone than actual wording. If you sound hot and bothered when using could, your request will sound impolite regardless.
There's nothing wrong with using either in the family context you described.