When we moved, almost 5 years ago, we moved the cats first. It was the right thing to do. Butter (our stray Siamese boy) moved into a spare room at my future husband's house, overnight. He had his litter box, food and water, and stayed there for at least 24 hours, in a bedroom where there was a bed for him to sleep. Mimi, our precious old lady, who has died since then, came to the new house and went in the most spacious bathroom, the morning of the move, with her litter box, bed, food and water. As soon as the majority of the moving was over, Mimi was let out into the house and Butter came later that day. They both adjusted beautifully. We also had several dogs, and two of them (our Golden Retrievers, Lilly and Honey) went to the boarding facility for a couple of days because we didn't have a secure fenced area for them and Murphy, our very old Lab girl, stayed at my husband's house during that time.

It all worked out, but I think isolating the cats was key in our successful move.

Good luck to you.
Logan