The day of action was led by the airport police team, along with immigration enforcement staff, North Somerset Council and the British Parking Association.
One family reported they were told to take a taxi to a farm, where they were made to wait for an hour, before being instructed to go to another farm.
They waited there for a further two hours before they got their car back, police said.
Another family, with two distressed children, was also apparently stranded before airport staff took them to a hotel, a force spokesman added.