Maybe you could put them in those containers people use to move animals.
But of course first make those comfortable for them by putting in small blankets, rags and some food they like.
And keep talking to them, explaining that this is just temporary.
Animals understand a lot more than many people realize.
I have had both cats and dogs, never had any trouble. Just treat them as if they understood what you are telling them, because they do. And keep them comfortable.
Good luck. I hope it will all work out.
Does that work on mothers-in-law as well?
I have had great success with cats by using simple language with them, rather like ebonics, and repeating simple concepts. When we had to move house, I used two cardboard-box "houses" and a cat figurine, and showed them to our cat over and over for two weeks prior to the move.
Example:
"Mommy/Daddy/Kitty move house!" (move toy car from one house to the other)When the move actually came, she sat up on top of a pile of stuff on the console between us in the front seats and looked out the windshield most of the way 150 miles down the road."Kitty move house!" (move the cat figurine to the top of the car and from one to the other).
"Sofa move, kitty basket move." (move dollhouse sofa, dollhouse cat basket) etc etc, whatever your cat finds meaningful -- ours had a blanket and basket)
"New house good, good, good! Kitty new house! Kitty bed! Kitty food! New house treats!"
Repeat this with encouraging and upbeat vocal tones every day, stroking the cat if possible.