When is the best time to move? Unfortunately, there is no "best" time to move with your children. Unless you count moving only after you've discussed it with your children. Get their input about the timing of the move. Try to avoid making your word the law.
It'll be very hard for your teen if you decide to relocate during their senior year of high school, right before they graduate.
For your younger children, a move during the school year will allow them toimmediately go from one social setting into another. They'll be receiving more attention from classmates and the teacher as the "new kid." On the other hand, a summer move may allow your children to become better acclimated with their surroundings. This way they won't be thrust into unfamiliar territory both at school and at home.
Your children may not like the reasons for the move, but with good communication, they'll understand them.