Humans are social animals. Therefore, we want to please the people around us at some level. From what you have told us, I suspect that he hasn't really gotten a chance to figure out 1- that he CAN do the right thing and 2- how good it can feel when he does. So he takes out his frustration on smaller people because that's the dynamic he knows.
You can train a horse two ways. You can push it and punish it and dictate to it until it gives you the right answers. That horse WILL give the right answers because to do otherwise tends to be painful. However, it will only give you what you demand and it will be sulky if it retains any personality at all. The other option is to set it up to win. When you make a request ignore any wrong answers and praise any right answers. Make giving the right answer easy. That horse will give the right answer because it wants to please you which means that it will be far more likely to go above and beyond for you.
So in this case- if you see him doing something that isn't good, but doesn't harm your kids, he gets ignored. (If he messes with your kids he get's Mama Beared because that's just the way the world works) If you see him playing nicely with your baby or (politely) moderating an argument between kids or anything that is a GOOD thing, you take a moment to praise him in some non-embarassing way.
If that's their dynamic, a team would be tougher. However, he is going to have to deal with H's for the rest of his life, and he could start developing his skills now?