I know this sounds awful, however, I used to have a cat (Norton, female tortie) that truly hated going to the vet, in fact one of the vets told me not to bring her back in to their office. They said they would have to come to my home. I found that a little extensive, so I took Norton to a different vet and all they had to do was put on a tiny little mask that went over her eyes. As long as she didn't see what was happening she was fine.

My suggestion, however cruel it may sound is to get a mask for your kitties and transport them that way.

Good luck on the move.

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Traci