How worrying for you. As a teacher, i have dealt with lots of teenagers and their families with similar concerns- it is more common than you would think, particularly where blended families are concerned.
I think there are two issues here, the violence/bullying and the cause of it. The behaviour needs consequences, longer term the causes need tackling.
Can you sit down first with your dh, the boy's mum and if she has a partner, them also? Take a step back from the situation and look at it from the bigger picture - this might be painful, but as adults taking a look at your own behaviours also. While it sounds dramatic to call it so, for a child, parents splitting up is a 'traumatic' event, and therefore the child has experienced trauma. He has experienced significant loss. Things to think about therefore as a group of adults (not to answer here on a public forum)
- how old was he when parents split?
-what was the cause of the split?
- how long before you and his father got together? How long before new baby born? (ditto if this applies also to his mum and her life post split)
- what is his role in the families? Does he have any say? It sounds like he is jealous of his younger sibling and half sibling. Does he get significant quality time with his parents without feeling like an added thought?
- what's he like when at his mum's?
-is he like this at school?
- like a pp said, could he have more flexibility around his contact time so it isn't seen as a chore but rather something he and his dad want to do? That way he can maintain his social relationships too (e.g could he be cheesed off that he is missing out on something this weekend as he has got to spend it at dad's).
- is he compared to his angelic sister by everyone? (most marking case i dealt with involved the 'devil child' and her 'gorgeous baby half sister' - these were the terms used in front of the children in a meeting about the former's behaviour in school).
- how could all of the above have actually affected him?
Once you have established a few home truths about everything, all of you need to sit down and discuss it with him and ask him also what he is going to bring to the table as a member of the families. You could use some of your own home truths as conversation starting points, but it needs to be done in a 'we cannot live like this, what can we do and what can you do' kind of way.
All this can run simultaneously to sanctions for his behaviour, but trying to figure out the cause will help find solutions longer term. Particularly if you can let him have some input too.
Wishing you lots of luck x