I just asked my mom, who was often complimented on how well-behaved and polite we three were. (I only tried to wrestle that gumball machine once, after all.) She says that you use the vocabulary with your children that you want them to use. You treat them the way you want them to treat others, and that includes speech. So, no, using words like polite and impolite is not "too formal." It's a way of instructing them to use words like "polite" and "impolite."
If I were talking to an adult, "impolite" is the word I would use, because I think it shows a certain amount of respect and intelligence. It's also the word I'd use with my three-year-old cousin because the meaning is appropriate, but it's more subtle than "rude" or "bad." If I tell him he's being bad, he gets upset. He knows what that means. He wants to be a good boy, but he's three and he doesn't know all the rules, and throwing trains at cousins is FUN. When I tell him he's being impolite, he gets serious, and calms down to avoid being "bad." He understands that "impolite" is a sort of warning while "bad" and "rude" both mean he's actually done something wrong.
Purely anecdotal evidence, I know, but those are my personal observations.
I noticed a sort-of theme in some of the answers about explaining things to children, which I agree with in principle, and my mom claims she once did as well...Until she actually tried it. She could try to explain things until she was blue in the face, and we would still just ask "Why?" And it seems to get worse the smarter a kid is. What do you say when a kid wants to know why the dirt from your shoes will get on the bench, or why there's dirt on your shoes at all? Are you really going to try and explain static electricity and all the other stuff involved (I admit, I don't actually know)...?
Personally, I have trouble explaining why my cousin's throwing his trains at me is bad. I have no problem telling him that throwing trains, or anything, at anyone, especially me, is very bad, and he should never, ever do it. Because I said so. And so does Mommy. And Daddy. Yes, I mean it...And no, throwing AT and throwing TO are completely different. NO! if you're throwing it TO me, you have to warn me!...I know it's not as much fun, but that's just how it works. Because I said so. Trust me.