When we had to put our cats down, my dad would always go around the house and remove the bowls, toys, and litterbox, so that my mom wouldn't have to. We had Blaze put down in May of 2020, and there hasn't been a new pet in the house yet.
I get the feeling mom is ready for another pet, but my brother Chris is trying to talk her out of it.
I told her that cats don't deal with change well, and if they are going to move in the next two years, they should wait until they're in their new place to adopt a cat.
Of course it's up to your parents, but I think a planned move is not a reason against getting a cat. We moved with our first cat. We kept her indoors for the first four weeks at the new place, then I let her walk through our new garden on a leash a couple if times before finally just opening the front door.
On moving day itself, I reserved one room in the new home for the cat exclusively; I put her bowls, litter box and her beddings in that room, locked the door and kept the key in my pockets, so that none of all all the helpers could let her out accidentally.
Cats are opportunistic beings, they can arrange with new circumstances and see very quickly where their advantage is and make use of it.
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