I think I'd do some homework to prepare for a fight.
If I were you I'd start looking at things like crime rates and the quality of schools in the community they're looking at versus where they are now. Give yourself all of the ammo you need if it gets ugly. If they're military, then it's not a long term move...try finding some information on the effect on children and moving versus stability.
I also agree with what Brock said. Kids won't choose the best parent, they'll choose the parent that lets them do what they want to do or is the easiest to run around.
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