I stay calm and say, "Sorry. House rules." Kids can't argue with the house. Staying firm even when I'm tired seems to be a big factor, too.
I also come down harder when people make my life harder. So if they argue after the decision is made, I make the decision worse for them, not better. The more they argue, the harder my life, the harder I make their lives. This seems to really work well. I get very little backtalk.
I do allow a period for debate sometimes before I've made up my mind. I like the idea of teaching them when discussion and persuasive speech is acceptable. But once the decision is made, further talk is prohibited.
The "Bossing me around/That's rude" stuff would be met with a time out or some other such discipline. When they pay the bills, they get to make their own decisions. Until then, there is a clear hierarchy and I'm at the top of it. That's not EVER open for debate. If nothing else, the law says that I am responsible for them!
