If they were on the wrong flight then it meant their names would have to have been forced into the check-in system by the check-in agent.
The only way this would have not been the case is if the travel agent that booked the flight for the family had made the error and booked the incorrect flight for the family.
I am not sure if i am correct but im sure that not every day the flights are a common check-in for thomson.
When the family turned up at check-in didn't they get asked which destination they were traveling too? Plus when the boarding call is announced and the gate pops up at the screen next to their flight. Once again at the boarding gate the boarding staff put out a gate announcement with the flight number and destination.
I would say that the origional error was by the check-in agent but the family had many ways to find out along the system that they obtained a boarding car for the incorrect flight.
I have to say that this is not the first time it has happened at cardiff, as summer last year First Choice passengers were checked in on more than one occasion for the Onur Air flight as there were two flights departing to the same destination an hour appart (on sundays).
I am very shocked in how this actually happened but would be interested in knowing the full story. (Technically this was a major security threat).