I think maybe one of the problems is she DOES know that you are going to go for custody eventually and so is being as unreasonable and hateful as possible just to dig the knife in a long , long way and cripple you financially and emotionally so that you stand less of a chance.Like a big power trip.
When I got divorced from my first wife I had to practically "buy" custody of my kids, as she knew that that was all I was interested in , so she ended up with all the money, the house, cars, you name it and in return I ended up with custody of my boys. People who have once been close to you have an uncanny knack of knowing what you are going to do next without being told and of being able to stick the knife in, in particularly nasty ways, and if she has an inkling he's after custody in her own mind then she's going to be hell on earth and will be trying her hardest to turn the little girl round against him. She only has to put on a few displays like that and the court are unlikely to grant residency to you.
I don't know how caring this woman is of her child, but are there any incentives that you could use to get her to be more co-operative? Is she just using the child bitterly or does she genuinely love her? If she genuinely loves her and is acting this way because she's massively hurt and damaged ( for whatever reason, not blaming your bf there) then you are on a loser to nothing to be honest. If the use is cynical however ( as was the case with my ex wife) then you might be able to twist her arm with a better financial or property settlement. It's a horrible messy situation and I can't see an easy way out Pink, I'm so sorry.