The only acceptable level of abuse in a relationship is none.
Are you in the UK?.
Was it his idea in the main to move to where you now are; if so that was also his tactic to further isolate you socially and emotionally along with keeping you away from family support or support of any kind.
There is help out there for you, you need to be brave for yourself and make some phone calls. Womens Aid and the Rights of Women organisations can and will help you here. The police would also help as well though you may well want to talk to WA first of all.
You cannot stay with him any longer, you and in turn your children are not safe in his presence. He is violent and solely responsible for his behaviours; you did not drive him to do this to you. What happened to you is not your fault in any way - this is all on him and his actions too are about power and control.
Please get your injury documented with the GP; this will also help you go forward. This could and likely will happen again to you. The nice/nasty cycle of abuse is a continuous cycle.
He could have all too easily ruptured your stomach all too easily and put you in hospital.
AM courses are no answer to domestic violence which is what you (and in turn your children) are suffering at home. You can only help your own self and your children ultimately. You deserve a life free of physical abuse.
He like many abusers, is probably quite plausible to all those in the outside world. He does not go around hitting work colleagues in the stomach does he; he would be out of a job and arrested if he did.
He has a problem with anger, your anger when you rightly call him out on his behaviours. Your children as well cannot afford to grow up seeing such an abusive example of a relationship, this cannot and should not become their normal. You cannot fully protect them from his abuses of you as their mum if you and your abuser are under the same roof.
Abuse like this, like you describe, thrives on secrecy. Do not keep this a secret any longer; start opening up to other people now. You are not as powerless as you think you are. Keep posting here too.