I have read your other thread and the replies on that too.
I would agree with the overall consensus on there as well; your H is a bully and your son is mimicking the behaviour towards others that he is being shown by his Dad. Its extremely damaging for children to be any part of this and the way forward from this is to actually separate.
What your mother has commented is completely unhelpful at the least as well as totally irrelevant (her comments say an awful lot about her); she does not have to live day to day with the fallout from your H.
I doubt very much that your H knows what love is let alone love the children. Well you would like to think that he loves them but he truly does not. He sees them like you; mere possessions to use as he sees fit.
What if anything did you say to your H when he came out with the "smash his face in" comment to your son?. How did you react or did you do/say nothing?.
You cannot act like a deer caught in the headlights here; you are going to have to act to get this man out of yours and your children's day to day lives. Seek legal advice as to your options from a Solicitor asap.
Think too you've probably been waiting long enough now for him to supposedly improve; you do not have to make your bed and then lie in it as your mother is seemingly suggesting. Your children are getting the emotional fallout from their Dad's anger. Also you write this man is (unsurprisingly) not very nice to you either and is both needy and difficult. This is more than enough to grind any person down (that's what he wants; for everyone else to be as unhappy as he is).
He is dragging you and his children down with him. Living with the Dominator is no picnic for you or for them either. These men DO NOT ever change and he is well beyond going to any AM class; its too deeply rooted within them.
What sort of childhood do you want them to have?. Your son is already in trouble at school and that may well be due to his Dad's behaviour towards him at home too. His sister is also being affected by all this at home too.