Emmy,
I read your story and it sounds like my story although my husband hasn't hit me but all the other stuff is just the same.
We are single mothers even though married. Our AH/addict husbands aren't around and aren't helping. It is actually worse when my husband is around because he yells at the kids or he is inconsistent, giving them mixed messages. My two children love their father too but I am getting to the point that I have to protect them and myself from his craziness. I think you may be at that point too.
You can do it. My husband's mother and father were both abusive alcoholic/addicts when he was younger. I see the damage to him that they both did. It doesn't excuse what he is doing now, but I want my children to have a fighting chance at not continuing this cycle.
Your children can see their father but he isn't good for them, nor for you. To be screamed at and threatened in public? To have him swipe his finger across his throat in a threatening gesture WHILE THE POLICE ARE THERE?! He sounds very dangerous. You have supportive family. You deserve better and your children deserve better than to see their mother belittled in public. Hugs!!!