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I have a daughter that lives in Alaska with her father, but she does not want to be there. We have asked him nicely several times if she could move here, to Florida, to live with me, yet he refuses.
Can my daughter, who will be 15 this January, choose to live with me?

What state issued your custody order?

If it wasn't Georgia, no, your daughter cannot choose. However, at age 15 most Judges will give a child's wishes some consideration, although it will be totally up to the Judge. You can file for a change of custody and you'll need to prove to the court that the change will be in your daughter's best interests.
Get a consult with an attorney in whatever state the order is in to get a complete idea of how likely your chances are.

Gabrielle is correct. You do need to consult with an attorney. You can locate one through the attorney locator on Lawinfo's home page at http://www.lawinfo.com/. Some do offer free consultations.