It all boils down to basic socialization and emotional maturity, and manners and principles.
Teach him these things now, before he gets older.
Also Google Search "Tween Boy Development" and "Teen Boy Development," since this is your son's developmental age, now.
Kids change a lot, at these cusp ages.
Many developmental stages, still.
But he is old enough, to learn basic human coping-skills for any emotion he has.
Even many adults, don't know this.
It is a taught, 'skill.'
Kids are not born with it.
At home, is often where kids let it all hang out.
Luckily, your son does know how to be nice, at school.
At home, is where he needs to learn, boundaries.
He also has his own interests and personality.
But learning 'cooperation' is a very important ability for him to attain. Still.
AND he has to learn that BULLYING IS SISTER... is NOT allowed.
Siblings, should have each other's back.
Teach him this.
Your HUSBAND also has to be a part of this. I don't know why he is saying that you & your son have to work it out on your own.
That is your Husband's son too. A boy, NEEDS direction and nurturing from their Dad, too.
Build a 'relationship' with your son.
See who he is.
He is a kid.
No matter what, a child needs his Mommy.
Don't be afraid of him.
This is a good link:
http://nymag.com/news/features/27840/