This is hard stuff with an innocent child in the mix. It's SO hard for a child to be separated from their mother. I'm not sure why custody was ever an issue and so wish that your partner and his ex could have gotten through coparenting peacefully. That's the goal. And whatever you have to do to make that happen, everyone will benefit. You may need to back off for a bit. Usually little ones adjust better than middle age ones or teens. But this is a complex situation with parents fighting in court. That's never good and takes its toll. Put a smile on your face no matter what. Don't try to be mom to the little girl and kind of take a back seat for now. And have your partner express to his ex that he wants to work together! He got with you pretty quickly it sounds after that break up and I don't know the history but break ups are always shard. And she may be entitlted to feeling bad. I agree that bringing it to a toddler in terms of having them emotionally involved with the negative aspects to it is wrong. but you can't control the ex. You can only control yourself.
Very true that relationships where kids are involved from prior relationships end because of the extra things people have to deal with. And if this is too hard and hurtful to you, that may be the best answer although it probably feels like a shame if you have a good relationship otherwise
But the little girl is not to blame. She's 3 and trying to survive the adult world of break ups and hurt and shifting houses/homes and people fighting over her, etc She's too little to be mad at for this. She needs TLC. For real. Good luck and I know it is hard. I hope it has a happy ending for you whatever that may be. hugs