You dont have to leave if you dont have too. Now if you are in danger of being abused or the children are being abused, you can either leave and go to a shelter or file a restraining order on him then a permanent which will keep him out of the home but not you until you can work thing out. Divorce, CS and so forth.
By law if you reside somewhere for more than 30 days, and that applies to whom ever, the other party will have to formely evict you, as wife and husband eviction will not work but legally because you have children, he will be kicked out before you and the kids are. Know your rights and stand by that