There is no magic age when a kid gets to make all the decisions. If there is a parenting plan and the other parent thinks the child should live with him/her, then they need to go to court to ask to modify the parenting plan. A court will listen to the opinion of a child who is sufficiently mature enough to express a reasoned preference, but nobody gets to dictate to the court what will happen.
Obviously, once kids get into their later teen years, they are far more independent and likely to "vote with their feet." If the child in your case is not 15+, it would be a good idea to have some counseling to nip the problem in the bud. Kids often don't understand that the reality of living with the other parent is way less fun and exciting than visitation weekends.
The court may consider the opinion of the child concerning their placement. However, it is merely a consideration. In NC, the opinion of a child is given more weight as they get older starting at about age 9-10.
The decision is up to the parents. If the parents can't agree, you will have the opportunity to mediate under NC law and then have a hearing. The judge will then decide the best custodial arrangement.
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There is no magic age when children get to decide where to live. The best interest of the child is the standard.
The law regarding a child's 'right'* to choose is a matter for each State and jurisdiction. The judge in most States, not the child, makes the decision based on the best interest of the child. Although not a standard by any means, many States have begun to give 'consideration' to a child's declaration of custodial preference when the child reaches the age of twelve or thirteen, sometimes fourteen. There are even cases when children of age 9 are allowed to testify.
The judge is normally given almost unlimited latitude in whether or not she or he listens to a child and how much weight to give to the child's wishes. In short, there is no specific "age" but the younger the child the less likely for a judge to give the stated preference much weight.
Good luck to you.
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