I agree with everything Jen says.

But we don't know the why of her not moving cross country with them

Ruffles moved in with her first owner, Peggy,as a kitten. She lived with Peggy 10 years, unti Peggy died. Then she moved in with a good friend, someone she had known as a visitor, Lucy. Ruffles lived with Lucy until she was 12. Lucy alread had a cat of her own, Topaz. Lucy was moving into senior housing. The only permitted one cat. Ruffles needed a new home. I agreed to take her in. She had never met me before. At that time, I had 3 other cats. Lucy came over one Saturday with Ruffles in a carrier. We opened the door and Ruffles came out and ran behind a piece of furniture. Lucy stayed 2 hours. Ruffles refused to come out and Lucy finally left. Ruffles never saw Lucy again. (I keep in touch with her.)

Ruffles was very depressed for 3 months. She spent her days on the foot of my bed, with a sad expression. Nothing I could do seemed to help. At night, she slept in that spot. She ate enough to keep going, may have lost a bit of weight but nothing noticeable. She got off the bed to eat and use the litterbox. She never left my bedroom unless I carried her out, and then as soon as I finished petting her, she did a slow sad walk back to the bed. The other cats got used to her as a bed object.

After 3 months, one day Ruffles got off the bed and left the bedroom. The other cats were quite alarmed! IT MOVES! Since then, she has adjusted very well, moves about the house at will, jumps in laps and insists on her share of petting, even has to check out the cellar at least once per day to make sure it is still there. Ruffles has lived here 2 years now and is fully integrated with the family.

I would really worry about an older cat being dropped off in a new setting with no one home, based on how Ruffles reacted. Dad and I were both home bodies during those 3 months of Ruffles transition. The cat will adapt at its own pace, not at whatever pace you want / need to set based on your schedule.

I don't know if this helps or not. This is just one cat, one move.