I think that parents have an obligation to teach their kids how to negotiate respectfully. Name-calling and physical violence are not optional ways of communicating. It is up to YOU to make that clear. When you see such behaviors, let the kids know (as if they never heard this from you before) that the have to solve their problems with proper communication - give them some examples. This will be Step 1 of the 2x-Rule. The next time that they fight after that, repeat your little lesson and give them a warning: "from now on, when you hurt each other with verbal attacks or physical attacks, such & such consequence will happen." Name the consequence. It can be a loss of privileges, a writing assignment or anything that you feel will act as a deterrent. Then, on the third occasion of fighting, give a consequence to any child who has been verbally or physically abusive. Use the same consequence for three or four more fighting episodes to see if their behavior is improving. If it isn't, change the consequence you are using to one that you think will have more effectiveness. Continue until you find the "right priced ticket" - the consequence that changes the behavior. Be determined and consistent and their fighting WILL end. At the same time, when you do see your kids getting along, comment on this delightful behavior. "So nice to see you guys getting along," and other small acknowledgments will be sufficient. If you want to really empower your praise, add a "reward" for cooperation every once in awhile. It can be subtle. For instance, you can say, "it's so nice and peaceful in here. Would you guys like a treat tonight after dinner?
Just mentioning a pleasant event somewhere near the compliment for peaceful behavior can have a positive effect on the brain, increasing the chance of cooperative behavior occurring more frequently.