Anger, frustration and empathy

Matthew and Jonathan have an odd dynamic when they deal with issues of frustration and anger, and I wonder whether we're alone in this.
The boys are getting older -- they will be six in eight days -- so I will not apply names to their specific behaviors. I feel I need to change the way I write about them as they age to protect their privacy in ways that will matter to them in the future.
But here's how it works.
One twin has a harder time than the other dealing with losing or not achieving his goals.
He gets mad.
Boy does he get mad!
He yells and stomps and hollers and, if some unfortunate Wii remote or game piece happens to be in his hands, he throws it. But he rarely hurts people. His anger is directed at himself and the particular challenge.
As we struggle to deal with this -- giving time-outs, talking with him, refusing to play with him unless he calms down, prohibiting certain trigger games for a while, offering him de-stressing techniques, tearing out what remains of our hair, gulping that glass of wine -- we face another obstacle.
A 60-pound, four-foot-four obstacle.
The other twin instantly reacts to his brother's emotions by hitting him or pinching him as hard as he can. If we're not in the room, it turns into an all-out brawl.
The offending twin doesn't know why he does this and can't seem to stop himself.
It could be because he knows his brother's behaviors will bring an end to the fun, and we've tried addressing that. We've tried continuing the activity with the other twin (after a time-out for hurting his brother, of course), but he does this even if he's not been involved in the activity.
So I'm wondering whether it really has to do with their immediate and obvious impact on each other or whether it's like their other empathic reactions -- they way they each get upset when the other is sad, or plead for the release of the twin who is in time-out, or refuse to sleep in our bed when they wake during the night for fear of leaving the other twin alone.
Maybe the one twin just can't stand the strength of his brother's emotions, so his tries to stop him for his own sake the only way he knows how. He reacts this way during play dates, but not when his brother melts down in school.
Instead, he steps back in school, away from the staff and other students who are trying to calm his brother down. My guess is that he controls himself because of the environment. We tend to let loose among those who love us unconditionally, like mom and dad.
We are working with the twin who has trouble losing. He is making progress, very slow progress at home and a little more progress at school, but nothing we do alters the reaction of his brother.
Still, in the midst of chaos -- flying Wii remotes, pinching fingers and time-outs -- I find myself intrigued, wondering what inspires him to do this.
Why can't the one twin allow his brother to experience frustration on his own?
Why can't he just let him be angry?
I'm baffled.