If he wishes to stay involved in her life, and you feel that he would fight the adoption, then most likely he will, and you have to be ready for that. As it stands right now with him having contact with her on a 'regular' basis, the courts are not going to be very willing to terminate his rights, there has to be just cause to do so, and her being homesick while she is there ( which is what he will most likely argue is the issue) is not going to be seen as such.
You could try to sue him for child support, and he may then be willing to sign over his rights in order to get out of having to pay. Even if he is not willing to his rights away, you will end up with more money, but he could in turn sue for more visitation. Courts now a'days are not as willing to do full custody, as they want the child to be able to see and have both parents in his or her life.
If you are feeling as though it isn't worth the big fight that you are anticipating, then that would be your answer. Give it some time and see what happens, sometimes parents get tired of the day to day struggles of long distance parenting and walk away on their own when you least expect it. Begin to document how often there is contact and how your daughters behavior is at home and at school both before and after contact. If you do decide to go to court for an adoption or custody, documentation can go a long way to helping a case. Make sure that your notes are well organized, and as unbiased as possible. If your ex does something well, or right then give him credit for that. If everything is simply negative the courts can take it as simply a bitter ex going after the other ex.
Stepparent Adoption Blog