It will depend on the maturity of the child and the reasons for wanting what she wants. Some judges might not even be willing to interview an 11 year old child at all. Other judges will give careful thought to what she says. This is a very tricky situation. Ideally in preparing for a meeting with judge you would spend time figuring out what your child's feelings are with her and helping her figure out how to make the best case to the judge. This is a bad idea that can horribly backfire. The other parent will, no doubt accuse you of alienating the child from them through your actions in even asking for a modification of custody or visitation. Your running to court to eliminate all contact with the other parent on just the child's say so might also be seen by the judge as alienating the child from the other parent.
If you are interested in actually filing for a modification your best bet is to have your lawyer ask the judge to appoint a guardian ad litem. The GAL will interview your child and determine her best interest. In doing so the GAL will take into account what the child wants and why she wants it. You and the child's other parent will also be interviewed. The guardian will then present his or her findings to the court. Your attorney can ask the judge if he would be willing to interview the child. You should NEVER bring a child to court unless that child is to be interviewed or is testifying in some manner.
All in all, it will likely be difficult to completely cut a parent off from all visitation altogether. After all, the other parent has certain rights too. A change in custody supported by sound reasons and the child's desire would probably be more feasible.
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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