Sorry, but I'm picturing the things you describe and I think they're hilarious... not in the way Sister thinks they are, but in a sort of cringe-worthy sitcom scene way. Where I am definitely laughing at
the character and not with
Sometimes my dad makes embarrassing comments in public. Like trying to speak in a certain language at an ethnic restaurant. When he has nothing to do with that ethnicity, knows nothing more than the one word he said, and has no reason to think the person he's talking to knows it, either. Even better when it's the wrong
language for the restaurant.
I usually either roll my eyes and move on, or sometimes I say, "Dad!!!" in that sort of put-upon daughter tone. I do these things in an obvious way, especially the latter, if the comment is goofy enough that I'm afraid people will worry that he's some weird old guy out wandering the town by himself. Sorry, folks, I'm trying to supervise him, but it's tough,
is the message I'm trying to send.
If your sister is making confusing comments to, say, a waitress, I think it's okay and even important for you to step in, because the waitress is kind of a "captive audience" whose job is basically to keep you happy, and it's rude to toy with that, I think. Maybe something like, "Oh, don't mind her. What's your soup of the day?" If your sister complains, maybe you could say that it's rude to take up the waitress's time/strangers' time with jokes (which is also true).
As for the police thing, IMO anyone who tries to joke with/about the police while they're actively arresting someone is on their own and I would probably just walk away from them--I respect the police and I'm not going to distract or antagonize them when they're doing their job. (I'm assuming Sister spoke loud enough that the police officers could hear her, or at least knew she was talking about them.)