I used to get the train into town (paying half fare as I was 13!!! I took my birth certificate) and then promptly went into "Follies" nightclub for over 18's! I always looked older than my age.
My parents however, didn't have a clue but when I told them years later, they were ok about it!
That was late 70's though and there wasn't the same drink culture back then..infact I can't recall drinking any great amounts..it was more like a social outing, meeting pals etc.
I can understand your concerns ginger and your Mum is being naive at the least.
What you do not say in your question is whether your sis is out during the week, or is it just Fri and/or Sat? Is it interfering with her school work? Is she coming home plastered at 4am?
It is technically illegal but apart from my fabulous, sensible husband I know not of any other person at 16 yrs, who hadn't been in a pub/nightclub!