You say it's not right that she doesn't have a bed that's her own.
However her father may be a crap husband, but he's still her father. He'd be entirely within his rights to go to court and petition for 50/50 residency, and then she might have her own room but frankly, you'd feel much worse.
I appreciate that what he did to you was bad, and what was done to you in the past was bad. However part of being a parent is seeing your child as a separate entity.
Your daughter actually has a significantly lower chance of being abused or unhappy n later life if her father is present in her life (yes, even if he's a bit of a rubbish one, so long as he's not abusive or dangerously neglectful). Annoying his partner and trying to stop your DD staying with her dad will likely make everyone, including you, worse off in the long run.
This is one of the hard bits of single parenting. Many or even most of us have to grit our teeth so hard, so often, to be a positive or at least neutral co.parent.
But you're clearly a loving mother, and you need to trust in all you do, and in her. To give you more confidence, it might be a good time to see a solicitor or at least look up more guides online to see if you can get something a little more concrete worked out for your sake and also to give your DD some more routine.