@maripiggy,
I have had cats myself so I can understand. Yes, they like familiar surroundings and can get stressed when you move, but they adapt. I've done it when I moved. They get used to after a few days, the cat might hide for a while or maybe not it depends so much on the particular cat's personality -- some are very curious and others are more skiddish.
In any case, if it is your cat, and you really want him, take the cat with you. If your mom wants company, why not get her a new cat? You can go to a shelter and ask which cat would fit in well with your mom and her personality. If you adopt an older cat, the shelter would likely know the cat's history and personality and could find one that would fit her nicely.
Bonus you give a cat without a home a new home and your mom will have her own cat for company.
PS - my mom went out and did this on her own. She said when all the previous pets passed away she wouldn't get another (all the other pets were one of us kids' pets that couldn't bring them where we were moving). She loves the creature and he loves her. she got him for mousing purposes but he is her baby now.