At 12 and 17, I hope by now this is a non-issue with my children, as they have had YEARS to learn what I expect in public and at home!!!!!! They do squabble a little bit at home, although much, much less than many of my friends' children. I think it's because they are five years apart, and therefore there's not really any "competition" for the same things - their lives and the things they are interested in are too different. Now, I will say that being preteen and teenage girls, they are both occasionally moody, but I expect that and we deal with it. After all, I'm moody too sometimes!!!! They know that I'll put up with a certain amount of muttering and one or two door slams, then it's in your room to work off your sulk by yourself.
With my friends and in public, they are delightful. I told them early on, "Look, most of your friends are going to mumble and not look at someone talking to them. You can be a thousand steps ahead in the game if you will just make eye contact and smile when a grown up says hello to you. It's just that simple." So they tried it, and gee whiz, it worked!!!!! I have people tell me all the time what nice girls they are, and it's really just because they know to say hello, smile, and make eye contact. It makes a huge difference to me when I meet someone else's children. If they can look at me and say, "Hi, Mrs. DVCLiz" that's a MAJOR plus. So many kids can't seem to do this.