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There isn't a specific statute that deals with this issue. If there is a court order in place, the child has no ability whatsoever to choose not to comply with it until the child becomes an adult. This is because the court order is directed at the custodial parent, not the child. If the custodial parent doesn't turn the child over to the non-custodial parent - whether the child wants to go or not - the parent is in violation of the court's order and could be fined and/or jailed. See Cal. Code Civ. P., Section 1209. The parent is expected to be able to ensure compliance with the court's order until the child turns 18 and is legally an adult.
If the child does not want to spend time with the non-custodial parent, it is up to the custodial parent to request a Modification of the Custody Order. The modification must be based on a material change in circumstances. The judge will determine whether modification is in the child's best interests. What the statute says is "If a child is of sufficient age and capacity to reason so as to form an intelligent preference as to custody or visitation
, the court shall consider, and give due weight to, the wishes of the child in making an order granting or modifying custody or visitation." Cal. Fam. Code, Section 3042. So, there isn't a specific age in the law. If the child is a teenager, the judge will grant more weight than if the child is a three year-old. What the judge will do is determine whether the child is old enough to understand the difference between the truth and a lie, ask which parent the child wants to live with, and attempt to determine why (if it's because one parent lets the child eat only candy, for example, that's relevant). Here is more information on requesting a modification, with forms:http://www.courts.ca.gov/1187.htm