The reason a passport can be withheld for failure to pay child support is because there is a specific law that provides for it. Usually the federal government doesn't care about state court matters, but someone passed this bill so they can withhold passports for THIS specific reason. Outstanding parking tickets? Arrested for something? No. Other than that, states control their own licenses and requirements, but if you owe child support in California you might be able to get a driver's license in Georgia if those two states don't have an agreement.
However, state courts and the federal law enforcement, including homeland security, do work together to enforce warrants. Arrests are OFTEN made as people come back into the country because that's when you run into customs. On the way OUT of the country, you show your passport to the airline people, the ship people, the customs people from the foreign country. Coming back? USA all the way.
Usually a person is held on the warrant where they are arrested, and the authority that issued the warrant is then asked if they want to transport the detainee, because the cost does go to the warrant issuer. Is California going to transport over $85? Unlikely. Is the next county over in Florida? Maybe.
The fine itself is no longer the issue so it doesn't matter if it was $85 or $8500, it's the Bench Warrant. The warrant has to be quashed (dismissed) before she can be released.
Nancy