This would not work for our cat at all, but I’m very much enjoying reading about everyone else’s intrepid and sociable cats!
Ours needs to stay at home and have her preferred cat sitter come in (she hides from all the others we have tried).
Even then, she will get a bit stressed if she sees signs of imminent departure like suitcases appearing, and go and hide somewhere inaccessible. (Our friends’ cat hid inside their sofa shortly before they planned to leave for the airport, via the cattery. They had to take a saw to it in the end, and take a late flight).
Getting cat into the carrier is a massive performance involving at least two people. We have to start trying to catch her at least half an hour before we are due at the vet to ensure we don’t miss our appointment. It’s the only time we use the carrier, so she would think we were going to the vet - which she absolutely loathes - so the journey would start on the wrong footing.
I’m sure she would wail mournfully for the whole journey. I’d worry she might manage to break out of the carrier through sheer determination. I’m usually a bit worried about that on the two minute drive to the vet, let alone a 2.5 hour journey. She certainly wouldn’t sit nicely on anyone’s knee - she doesn’t even do that much at home!
She would be furious with us, and absolutely terrified when we arrived, and this would probably translate into hiding somewhere unhelpful like behind the washing machine or under a floorboard or something, and refusing to come out or eat for the whole trip.
She can open doors by jumping on the handle, so I’d be constantly worried about her escaping.
Then we’d have to do the whole ridiculous shebang in reverse to go home. Possibly starting by dismantling the whole kitchen of our long-suffering hosts to get at her hiding place.
Cat sitter all the way for me!
The cat shows a bit of vocal displeasure when we get home from holiday, but it’s usually all forgiven after a peace offering of a bowl of food and some contrite strokes.