You have a couple of options. First, you can file a Rule to Show Cause with the court that currently has jurisdiction over the existing custody order. The NCP will need to be served with the Rule in order to be held in contempt and/or for a capias to be issued for the NCP's arrest in the event of failure to appear at the Show Cause hearing.
You should be able to effectuate service in the other state via use of a private process server under VA's long-arm jurisdiction statute (I'm assuming it is a VA custody order and that the CP and child reside in VA). You may also want to set the Show Cause hearing for the same date, time, and place as the currently scheduled appearance for non-payment of child support. If the NCP is a no-show for these proceedings, then the court will issue a capias (bench warrant) for the NCP. However, unless the NCP is caught in VA by the police with an outstanding warrant against him/her, nothing much is going to happen as a practical matter -- the state just doesn't usually spend the money and the man power to track down and extradict people for these types of matters.
So, if the Rule to Show Cause does not result in the NCP appearing in court and returning the child in accordance with the court order, you will want to take the fight to the NCP -- so to speak. This is done by registering the VA order with the court in the NCP's state for enforcement. The NCP will be served with notice of that proceeding and if they do not appear and/or produce the child, then that state can issue an order directing the polce to go arrest the NCP and procure the child. This is a basic, general explanation of the process, as each state has its own particular rules and procedures -- though all but one state, I believe, have adopted some version of the UCCJEA (Uniform Child Custody Jurisdiction and Enforcement Act) which governs these types of matters. If you need to go this route, I would strongly urge you to find competent counsel in the foreign state to handle that matter on your behalf.
This response does not create an attorney-client relationship and is intended for general information purposes only.