Does your ex wife "deserve" this favor.
What were the circumstances surrounding your divorce?
We co-parent well, we haven't had many problems. If one of us wants/needs to change the schedule it hasn't been an issue. She a good mother and I know she would take good care of our child. She did admit that she wouldn't be able to do it if the situation was reversed.
We divorced because we fell out of love and couldn't, or didn't want to, get it back. There wasn't anything that either of us did, really, we just were not right for each other. We married because she was pregnant. When the time came, we both agreed that divorce was what we wanted. It was amicable. Painful, but amicable.
You and you ex seem to be working co parenting well.
I would do it, depending on how long they were gone and ask the daughter does she want to go, is the option open to let her stay with you and not go with them and the ex get extra summer and holidays?
They would be gone for 3-4 years, 3 years is the minimum. 4 years appears to be more typical. I have a family member who was stationed in Germany. He was suppose to be there for 4 years, 15 years later he and his wife are still there by their own choosing. I made it clear that IF I agree to this, 4 years is the absolute maximum. That would be brought up in court as well when going over custody.
My ex-wife has said that if the situation was reversed she would not agree to it. If our child does not want to go, my ex-wife would stay here and nothing in my life would change. My ex's marriage would suffer, and she'd have her new baby alone but those aren't really my problem.