(((((Mindfull))))) Been thinking about this today...
I think you need to let her fall. If she doesn't pay the rent, she gets evicted. If she gets caught with the fake ID, she pays the consequences. As long as you and H are there to catch her, she is going to keep on being irresponsible. If she ends up moving home, you need to set serious boundaries. I think that would include no drinking, and a curfew. She won't like it, but your house, your rules. Or give her a blankie and a pillow, and show her the door.