S.A.
I have some of that going on in my house, too, with 2 boys who are 8 and 5. They get along sometimes, then all of a sudden the 5 year old is stomping up the stairs and screaming at the 8 year old. Time away from each other is essential if you can find it. Since you are a stay at home mom, they probably don't have much of that. I am a teacher, so I am a SAHM in the summer, which is when the fighting started. They are better during the school year when they are not together all day.
Try doing something separate when your hubby is home - you take one, he takes the other. Something fun like a bike ride, swimming, getting ice cream...any diversion away. We do that around here when my husband has a day off.
I've made mine hold hands all the way home in a car ride to get them to shut up before. It usually works!
And don't feel bad about feeling like you want to just walk away. I feel that a lot, too, and I'm sure we aren't the only ones. Maybe you should! Get a babysitter and go away for the afternoon. Get a pedicure, read a book at the coffeehouse...Let them fight for someone else!
Good luck. I feel ya'!