Divorce with children

Any help I can get is greatly appreciated. At the beginning of this year my husband and I separated. In the beginning we had been getting along really good for our kids sake but now we are both dating other ppl and idk what happened but since his most recent gf came along (maybe 3 weeks now) He is the biggest most arrogant jerk. We fight about everything! In the beginning we agreed we would wait at least 6 months of dating someone before we even think about gradually introducing them to the children. Yet now he wants them to meet this new girl. I said that I don't approve and that he needs to wait in the best interest of our kids and their emotional well being. Well now he's even worse. He's threatening to hire some high priced lawyer and take me to court knowing I can't afford that since I only make 1/3 of what he does and he doesn't pay much in child support (we don't have any court orders for anything yet and we live in AZ)