The short answer is, "Maybe." California values children having strong relationships with both parents, and when one parent wants to move away with the children after divorce, maintaining those relationships can be difficult. This is a particularly complicated area of California family law, and the law is constantly evolving. It is best to consult a family law attorney who is well-versed in the law of custody and parenting time so that they can advise how current law applies to your specific set of facts.
In general, if one parent has primary physical custody, also known as sole physical custody, that parent has the right to move away with the children, unless the parent who is opposing the move can show the court that the move would not be in the children's best interests, or would be detrimental to the children. However, if parents share joint physical custody, the parties both must argue what they believe to be in the children's best interests.
In such a situation, the court is faced with determining which parent should now be granted primary physical custody as one parent is moving. These cases rely very heavily on the actual facts and circumstances surrounding the parenting of the children. The court will look at how long the children have lived here, if they are involved in extracurricular activities or have other family members whom they are close to that also remain here. Any and all relevant factors can be considered by the court. These cases rarely resolve themselves and typically end up in court at a contested hearing.
If one parent has sole custody, a "move away" situation requires the parent who wants to move to file a motion with the court for a modified custody order, or the opposing parent to file a motion for change of custody so the child can remain with him or her. At a hearing on the issue, If the parent opposing the move can provide sufficient evidence that the move would be harmful, the judge can order that the children remain here with the parent who is not relocating and make orders for visitation with the relocating parent.
At the evidentiary hearing on move-away cases, the judge would receive testimony and evidence regarding whether the move would be in the best interests of the child, or whether the non-custodial parent can provide the court with enough evidence to show that the move would be detrimental to the children. These cases are very difficult for the parents, and also for the courts. Regardless of the court's ultimate orders, the children's lives will be altered and they will not maintain the same relationship they were able to prior to a parent moving.