the violence escalates

I was reading an article in a scouting magazine yesterday about teaching your kids responsibility. One of their tips was to let kids work through their arguments on their own. I hate that particular tip. That may work for some people, but if I don't intervene in their petty arguments they soon escalate into violence. For example, my 2-year-old has recently begun referring to the character "Doc" from Cars as "Doctor". This infuriates my 5-year-old. Here's how it goes:
2-year-old: Doctor
5-year-old: It's Doc!
2-year-old: Doctor!
5-year-old: It's Doc!!
2-year-old: DOCTOR!!
5-year-old: IT'S DOC!!
SMACK WAAAAA!
SMACK WAAAAA!
MOMMY!!
mommy: silence
YOU HIT ME!!
YOU HIT ME FIRST!!
BANG CRASH BOOM
At this point I look in the room and discover the coffee table overturned, the couch cushions scattered about the room and both boys lying on the floor screaming and bleeding. My biggest fear is that my children will grow up and get jobs advising foreign governments. Can you imagine?
foreign leader: But I like the president of that country!
my child: Trust me! If you let him get away with mispronouncing the name of your dog, you'll never live it down in the U.N.
foreign leader: Okay. If you say so. I'll launch the nuclear warheads today.
my child: (with a self-satisfied smirk) It's all about being right.
Then we'll all die and it will be my fault for not intervening more when they were younger.