To Uniform Probate Code deals with the law concerning the affairs of decedents and missing persons. It would not apply to a custody dispute. If there is a custody dispute and you need a modification to an order dealing with custody, you'll need to file a modification law suit, which will be governed by the rules and law concerning domestic relations and post-divorce issues. It sounds like you need to talk to a domestic relations lawyer.
This answer is not intended to offer a legal opinion, to provide legal advice, or to establish an attorney-client relationship. Please contact a lawyer in your jurisdiciton to assess your legal claims. Most claims are subject to specific statutes of limitations. As such, it is important to assess your claims quickly so that you do not lose any legal rights.
In addition to what the prior answer said, you should know that most probate and family court judges discourage parents from having their children "speak in court" in custody cases. Your daughter's voice, if it is going to be heard in the case, will be there through a guardian ad litem (GAL).
Take a look at the issues involved in parental move-away cases in the link I have provided below from the Mass. Trial Court Law Libraries' "Mass. Law About ..." pages.
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Your goal is good, but your approach is bad. You need to go to court and file for permission, You may well need to retain a Guardian ad Litem.
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You need to file a Petition to Remove the Minor Child from the Commonwealth. It is always a difficult task given the dual pronged standard of: 1) a significant advantage to the parent, 2) in the best interest of the child. It is even more difficult since you have joint custody and presumably a history of cooperation in the parenting of the child and there is an established close relationship between your daughter and her mother.
You should retain an experienced domestic relations attorney — you will need his expertise to fight this uphill battle.
You should also consider crafting some form of visitation and parenting plan to maintain the relationship between your daughter and ex-wife, should you prove successful in your move to Florida.
This is not legal advice and is not intended to create an attorney-client relationship. You should speak to an attorney for further information.
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