Sweetheart remember him screaming at her to shut the fuck up as a tiny baby? Being willing to see her in a homeless hostel so as to get rid of all responsibility for housing her? Stealing from you by threatening not to give her back unless you let him? Lovely, how on earth would growing up in a house with a man like that, fulltime, and seeing how he treated you and seeing you fail to protect her from a woman who wanted to spend hours alone with her, end breastfeeding, and enjoyed seeing her cry be to her benefit?
Never doubt you've done the right thing. You tried to set boundaries to protect her and then he ended the relationship in favour of an OW. He's never paid his way properly as her dad. He's abused her mother. How is that a life any child should lead - should she grow up thinking that's all she in turn has any right to expect? Yes, they probably will try to poison her, but with limited contact she will end up making her own mind, and it won't do them any favours. The parent who is calm and doesn't throw accusations around or involve her in conflict, but who genuinely loves her, is the one she will remember as being there for her, and trust. You can offer her a calm, loving, stable and secure childhood in a lovely forever home now. You can offer her warmth and good boundaries and peacefulness. You've achieved that for her, and you should be proud.
This is such a hard time. But this too shall pass, and you will have a lovely life in the future. You just have to hang on in there through these bits, and try to enjoy the positives you do have - loving parents, gorgeous child, nice new home. It's all there and all real, which the relationship you thought you had sadly wasn't. He doesn't sound very capable of loving anyone, sadly, and probably learned that at his mother's knee. 