I agree with what the others have said. Kids want what they want when they want it (they're like little alcoholics that way). WE are the grownups and we don't simply give in because of tears and tantrums. Not that she isn't legitimately sad, it's just that acting out and crying and clinging are the only ways she knows to cope. You gotta be the mom, the one who makes her feel safe, even if she isn't happy with the changes.
I also agree that staying put is less stressful on everyone (of you, anyway--I'm not concerned about the alcoholic) than ping-ponging back and forth. If you file for divorce, you may be able to move back and he will have to move out AND will have to stay away from the house and leave you alone except for scheduled visits with the children, as the court may order.
You're in a safe place for now. You had good reasons for leaving, including his violence (which is MUCH worse for kids than having to move is). If I were you I'd stay put and get busy with looking for more permanent arrangements. Lots of people aren't lucky enough to have a safe and supported place to go to.
And I would STOP thinking about what impact your actions will have on his drinking. The only impact it will have is in his own mind. He can get sober anywhere if he wants to. If he doesn't want to it doesn't matter where he lives or where you are.