PePe LePew,
I'm so sorry to hear about how your husband is going through with the ex wife when it comes to their daughter, it's best to not bother with her anymore, have him go to court and get visitation rights or half custody of his daughter. His ex wife sounds like a very selfish and self-center person who only look after herself instead of putting her daughter first. She should allowing your husband have some connected with his daughter, whether by thousands of miles away from each others or not, she still has to allowing him to see his own daughter. But, your husband is responsible to provide her (the daughter) transportation to get her to come and visit you, or you can go there and visit her.
Once the judge granted your husband visitation or half custody rights, the ex wife has no choice but to follow along with whatever the judge made his rule. Even if it means that she has to allow him to have half of the summer with his daughter she has to granted you those summer with your daughter, she doesn't have a choice, even holidays too. Too bad for her, she plays games, she going to get played too.
Make sure your husband asked to see his daughter through VP or web camera as much he can to see his daughter also, make sure he tells the judge that too since you both live in different states. So, that him and his daughter can have a strong daughter-father bond.
Make sure your husband also tell the judge how his ex wife made false allegations against him and keeping him from his daughter. Judge won't like that trust me, because she is not suppose to put her daughter in the middle of her hate for your husband, it's between her and your husband, it has nothing to do with their daughter. Make sure he keeps every conversation that he had with his ex wife which involves his daughter, that would be evidences to provide to court to show how the ex wife is, her true colors.
I wish him all the best of luck, and hope it goes his way.