Uniform Interstate Family Support Act
The Uniform Interstate Family Support Act is federal legislation, and all states must abide by it. It requires that if you're divorced in one state and your decree includes child support provisions, every other state must recognize the court order and help to implement it. Therefore, if your spouse moves out of state with the children, the new state can and must collect your child support on her behalf if she requests this. She can register with that state's child support services, and it can work with your state if you're paying through government services there, as most parents do.
Domesticating Your Judgment
If your spouse moves to a different state, she may have to domesticate your divorce judgment in the new jurisdiction before child support services can get involved. This is a legal process that registers your judgment or decree with the news state and allows it to enforce the order if you should fall behind with your payments.