I think your Yummers should be ok. Several years ago, when my husband and I bought our house and I moved my Lucy cat, she was 10 years old and had always lived in the same place. (His cat, Crystal, had moved several times, so it didn't bother her).

Anyway - I did just what all of the other people recommended - I kept her inside for a couple of weeks (which wasn't easy, since she hadn't used a litter box in years ) Then, I started allowing her outside, but only with me right by her side. She adjusted very well, and after that, I could let her go outside and she never tried to go back to her old house.

Best of luck with your move.