Thanks for all the comments!
Everything could not have gone more smoothly. My dad dropped them off at the airport in Dallas with Continental. After filling out the appropriate paperwork, they were off to Houston. 2 hour layover in Houston and then into London Gatwick at 9:55am. We called at about 11:45am and they were already cleared! It sounded like they didn't have many animals, because they knew the cats as soon as we called. They referred to them as the GLASGOW CATS. We were surprised and elated that it went this smoothly and they cleared so quickly!
The ARC at Gatwick confirmed that they would put them on their next flight with BA which was at 3:45pm to Glasgow. They flew into Glasgow at 5:10pm but we were told to get there at 5:30, which we did....but when we arrived, they said it would be about 6pm when we could actually get them :/ 30 minutes of waiting in agony, but they finally told us to go downstairs and they would deliver them to us. When they brought out the carriers, Scotch (the white one) looked freaked out and she was crying. Kid was just slinked back in his carrier.
We cabbed home and voila, they made it! They immediately were running around and checking out their new place. Kid hid most of last night but kept occasionally popping back out. Today they are both as normal as can be and seem to be well adjusted.
All in all, I don't think it could have gone more smoothly. Lots of credit and thanks to everyone on UK Yankee that helped out with info! All the hard work paid off....