Your request isn't ridiculous at all. It can be really super frustrating going through this. The hardest part is keeping your cool when things run afoul, but keeping calm is the best thing you can do, because kids aren't comfortable seeing their parents "lose it."
You have gotten some pretty harsh responses. Hitting a child in the MOUTH?!? "Punish them EVERYTIME, and quickly, and don't worry about being too harsh"? For Pete's sake,
why not? I mean, punishment doesn't seem to be working for you, and NO ONE suggests stepping back and trying something different, just do more of what isn't working?
So, it's tough keeping calm when your kids go bonkers - it's tough for everyone! I like what Kristine S said about trying to model what you want them to do. It sounds like you were out of patience when your 11-year-old came in to talk to you, and it's hard to listen when you're angry, even for adults. But if you want your kids to learn to control their emotions, the best way is if they see *you* keeping your calm and not allowing yourself to get upset.
If you can manage to put aside your emotions and FORCE yourself to remain calm (remember that it's easier for you as an adult to do this than a child), then you can USE that opportunity for constructive conversation. Instead of saying "Not now, go upstairs" when your child comes to you, use that as an opportunity to model good listening.
And yeah, your kid is going to try to explain his side of the story, and probably say things that you disagree with, but... just let him get it all out before interrupting him, even if you think he is dead wrong. You don't have to agree with him, just listen. And when he's done, PROVE to him that you actually were listening (and not just planning what you would say next) by explaining to HIM how HE feels. (Like "It sounds like you are frustrated because you want to X and I won't let you. Is that right?"
(or "your sister doesn't give you a turn, or such and such is unfair.") But ALWAYS say "Is that right?" And make sure *HE* agrees that you *DO* understand. Again, that does NOT mean you agree with him, but it shows you were listening to him and took the time to understand his side.
Eventually he WILL run out of words and then you can ask him some questions that might get him thinking about other people's perspectives.
And once you've listened to him, you can say in all sincerity "OK, I've listened to you, and here's how *I* feel about... <whatever>." I think just opening this door will make a HUGE difference, and the main thing is not to lose your cool and blow up when they first come to you. If you can make it through the first 30 seconds or so, it does get easier.
Try and put yourself in your child's position. I don't know how the inital argument got started, but he was obviously upset when he came to you to talk, and when he got sent away, he was even more upset, and he probably also felt that no one understands him (AND he got punished for talking about it.) I'm not saying that to make you feel bad, just trying to get you to think differently.
There's a great book called "How to Talk so your kids will listen and listen so your kids will talk." I like that one a lot better than the "1 2 3 Magic" book, which basically says "Don't get upset, calm count to three to give your child time to SHUT UP OR ELSE!" What a way to shut down communication in the family! But at least they give you a way to avoid screaming at your kid...
And please don't think I'm bashing your parenting skills, what I've suggested is hard, REALLY HARD. Much MUCH harder than smacking a child in the face, or even just sending them to their room. But I hope it will be worth it. Good luck.