The obvious answer to this is that the the Dad should find his own place with his daughter. The OP has already said that he tried living with this GF before and it didn't work well, them living together, hence why he moved back into the OP's home. BUT he kept seeing the GF.
This is CFery of the first order of magnitude on its own!
He left his DD behind the first time he moved out. She whined when OP tried to give her boundaries and discipline, and her father, the man who had moved out and left her behind, STILL managed to undermine the OP by telling her she couldn't tell his DD what to do.
CFery of the highest!
Then he moves back in, and STILL makes no attempt to actually actively parent his DD, leaving it to the OP to do what she can, while being undermined, taking shit from the layabout DD, AND still trying to parent the 3 younger kids, all of whom can see the sterling example
of their older sister's behaviour.
And yet some of you holier-than-thous are still trying to suggest the OP has somehow done wrong, and should "step up"? Oh fuck off.
The only thing the OP has done wrong so far that I can see is to be entirely too nice to the massive CFer she had kids with, by allowing him to stay in her home.
Parenting teens with attitude is hard enough when they ARE your own, and you DO have parental rights over them - it would be an utter nightmare to attempt it with a child with attitude who already tells you that you can't tell them what to do because not a parent, and whose actual parent is a witless cuntweasel who can't be arsed to do the job.
@Pinkflamingoo - your ex is useless. Of course he should take his DD but he's not going to. She can't stay at yours - your 3 kids are going to look at her example and think this is the way they can do it too, when they're older - just no. She needs to go to her nan's, with her Dad, or into some kind of accommodation where they help her to stand on her own two feet, which I'm QUITE sure would necessitate her either being in education or getting a job.
Do please tell your witless ex that you will be reporting him to social services if he attempts to leave his DD with you, with no support again.