After school activities would also be too much for my 6 yo, so I can see that sort of situation happening. In that case, I'd probably go over to him, tell him that it's just been a long day, so we'd get the snack to go and skip music.
I really like what my DD's preK says . . .they say that in a difficult situation, they tell the child that they will HELP THEM when there is a problem. I try to keep that in my head: when my child is acting out, I say in my head: DD is having a problem doing ___. I will help her do ___ until she is ready to do it alone. In some way-- a hug, a reassurance that you are there-- convey that you will be there alongside your DC during this period of need. He's not going to have to deal with it alone.
For example, in the case of your boys fighting, I'd say something like "It looks like things are getting too rough between the two of you. Why don't we go do _____." You stay WITH him while he's having trouble.
As for the escalating/consequences thing, I find that the #1 most effective way to change this is to change my expectations. The closer I align my expectations with what my child is truly capable of, the better off we all are. Also, if you have the firm belief that HE IS DOING HIS BEST (I'm shouting because I constantly have to remind myself of this) then somehow, it gets easier. Less pressure on you both.
Finally, I find the less talking I do (not evident in this post!) the better. When DD yells at me and I ask something like, "Have you had a hard day?" then we usually get somewhere (vs. "don't yell at me!").
2/02, 4/05, 2/07, 11/09, and EDD 12/25/11