J.D. Lott and his wife Britney were eating lunch with their eight kids on April 30 when he missed a call on his cellphone. The family was three years into a cross-country, home-schooling, Instagram-documented road trip in a bus they refashioned into an RV. A day earlier they had been staying at a Florida campground. The next day, they were in Georgia on their way to meet friends—or so they thought. Half an hour later, the missed caller sent a text saying that they were from the Department of Children and Families (DCF) in Florida. It continued: "Please respond we...