The only thing I can tell you is that your husband should go back to the court order custody. Go back and read the papers carefully. If he is supposed to have every other weekend, then make arrangments for that to start happening. Don’t let any excuse work. Make plans for every other weekend and show up to pick her up. His ex knows that living out of state makes things more difficult and she is not going to help. The daughter is 10 so she should be able to make some “plans” too. Start with taking the original court order and arrange your schedules so that you just go get her every other weekend.
If the paper say that he gets half the vacation then get her summer schedule and pick either the end or the beginning, and send the ex those dates in writing. “I will pick — up on June x and return the child on July x”. Don’t send her a proposal send her a scheduled time. Don’t give her the option to choose not to let her be with her father. With the court papers, your ex was awarded joint custody. Take the time given because if it goes back to court, she can show that the visitations he was supposed to take was not taken. This may look to the courts as a reason to modify that custody due to lack of interest. Document everything, every time she refused, every time she caused problems.
Just because your husband has been told that other fathers only get a specific amount of time does not mean that he should settle for this. Take the time he’s supposed to with her. Her attorney would not take you back to court for following the court order or agreement…only to get that modified so that he has even less time. Joint custody normally means that both parents equally call the shots. It sounds as though he has been letting the ex make all the decisions as though she has primary custody. To let that continue would be a mistake, IMHO.