The information you received about a letter being written on your behalf is not true. While such a thing might be helpful, there certainly is something the father "can do about it."
The easiest way to go is with the father's consent. You can tell him about the situation and request his blessing to go. If he consents, then you are free to go.
If he refuses, then you would need to involve the court system. You would file a request to relocate with the court that handled the matter previously. Your pleadings would discuss what you've detailed here:
Assuming the father maintains his objection to the move, the court would ultimately determine whether you could move. The court would consider your reasons for the move and how the move would effect the father's contact with his children. Considering your husband's military commitment, my guess is that the court would permit the move.
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