We moved house a year ago now. One cat settled in right away, one we have to pick up from the old house on a regular basis, one never settled. After some time it was clear she really wasn’t happy so we rehomed her with some friends where she has fitted right in, being spoiled endlessly like the fat happy old lady she is.
All this last in first out is wrong IMO, you need to work out how to provide a good outcome for all, both of them could be rehomed with care and have a great life.
I would try an upstairs litter tray and ramp access to the window first tho.
Over the years our cat/s have got used to Great Danes, Wolfhounds, Ridgebacks, and Staffies.
Pecking/scratching order is quickly established in favour of the cat.
Our current aged cat has had more trouble adapting to my daughter’s 2 young cats which have just been dumped on us while she finds a new house.
I don’t agree that cats don’t care. It’s just they show it differently.
Our cat follows me and the Wolfhound out for a walk. She’ll go for about a mile and comes to a close approximation to heel if I whistle. Previous cats have done the same, and it’s off their own accord. We don’t try to get them to come along.