Generally, courts are reluctant to allow a minor child to "decide" with which parent he or she wants to live for the obvious reason that it is forcing the child to pick between parents; however, once a child reaches the age of 16 or 17, it is difficult to force the child to visit against his or her wishes, so the court will weigh heavily the opinion of a child of that age.
To "press the subject" you need to first stop discussing the issue with your son. If what you say is true of your 'ex' you could offer to continue to pay her the child support even through she is allowing your son to be with you more often. If that doesn't or won't work, you should file an Order to Show Cause for increased custodial time, and perhaps request that the court order either an evaluation with a mental health professional or appoint minor's counsel for your son. In that way, your son has a voice in the process and the court will know of his preference.
This is a nuanced process and you really should seek the assistance of counsel.
I generally agree with what Ms. Rutledge said, especially about needing counsel. Courts interview children and begin to consider their input as young as age 7. They place increased weight on a child's wishes as the child grows older, and most 16 or 17 year olds can write their own ticket. The major thing is how mature the child is. At 10 he may tell you he wants to live with you because he knows it's what you want to hear. He may be telling his mother something quite different. The way it works is you file a motion to modify custody and when you get to a Family Court mediator, you ask the mediator to interview the child and/or recommend appointment of an attorney for the child. Please read the guide I wrote for Avvo on preparing for a Family Court Services mediation - http://www.avvo.com/legal-guides/ugc/preparing-for-a-family-court-services-mediation-in-a-custody-dispute
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