Hi OP,
Your H sounds awful and the way he speaks to you demonstrates his lack of respect for you. I’d go further and say it’s not lack of respect but total contempt.
Ask yourself, does he speak to other people like this? Does he talk to his work colleagues like this? No, didn’t think so. It is you he directs this nastiness towards.
As for him demanding you apologise for your ‘violent behaviour’ - then he is either being a total prick or he is attempting to gaslight you.
And he is an arch-sulker. Because of this, I would not suggest you try to ‘out-sulk’ him, as I think he would win through callousness and his own righteous anger. He knows you have no reserves of energy (or useful friendships or money) to win on that...I think he would emotionally blackmail you regarding the children if you tried to ‘withdraw services’ from him.
Instead, understand that a person who treats you with contempt and hatred, does ACTUALLY despise and hate you. ‘When someone shows you who they are, believe them’ -is a Maya Angelou quote often used on here, for good reason.
Do not kid yourself. Don’t exhaust yourself fighting battles you won’t win.
Do whatever you’ve got to do in the house for you and the children. If he’s on ‘no speaks’ , well fine, that’s up to him.
Then tomorrow, research family solicitors and make an appointment with a couple of them. Pick the one who tells you they have experience of obstructive, hate-filled, border-line abusive or actual abusive spouses....get them to tell you where you stand in the event of a split.
Then - without telling him you have seen a solicitor or scouted your legal position - sit him down and tell him that you feel his attitude to housework etc is a deal- breaker for you and that you won’t continue being married to him if he is determined not to carry his share of family life....which includes day-to-day chores and sorting out the children. Tell him you do not want your children brought up in a miserable Home where one parent treats the other like a skivvy.
His reaction will be telling. If you just get more anger (which seems likely) that tells you that he doesn’t see why he should put any effort into your marriage and more particularly, is not at all bothered that you are unhappy.
If he is devastated, tells you that he never realised you are this unhappy, that he loves your dearly and he would do anything to save your marriage and bring your children up in an atmosphere of loving partnership from now on...well that’s nice, you can work from there.
He should love you OP -which means he cares about your wellbeing and happiness as much as his own. You are not there solely to maximise hiswellbeing and happiness! Yes, everyone has arguments,however, you are not talking about marital tiffs here but a long-term controlling strategy that he has decided on, which you have had absolutely NO say in. And expects you to obey him! That is not how reasonable people conduct relationships.
His behaviour towards you is shocking OP. You know that, don’t let your lack of nearby back-up stop you from considering a different future.
And you’ve got us now!