abusive men will always try to intimidate you, it is also a form of bullying...don't let him. He simply cannot walk away from obligations. get some good legal advice and empower yourself.
who the Hell is he to walk off and just leave his obligations and support? you have nothing to be ashamed of, but he sure does.
I hope that you can talk to your family and tell them the truth about his abuse of you, I hope they will take you seriously. get with the DV center and a lawyer and make sure that you tell your family you have done so, in that action they may take you seriously.