If your daughter is seven years old and there is no reason for the court to order supervised visitation (other than the reason that she does not want to go) then it is not likely the court will grant a request for supervised visitation. I would suggest that you speak to her father about what you are trying to accomplish. He should be understanding knowing she is having difficuly being around him when you are not present. You may be able to come up with some type of vacation or spring break planning where you could be there or nearby. If a modificaton is filed, you may have to work this out in mediation first (if the court orders it). So why not try to work it out amongst yourselves first.
The information provided is not advice but a legal perspective and you should schedule a consultation with the lawyer of your choice.
Wow! You need to talk with a lawyer.
A step up or supervised visitation sounds like it would be a logical condition. I have had many cases with situations like yours. Children that young flying alone are dis favored. If he is absent, it is like visits would be here and under supervision for 3 to 6 months at least.