you said your cat has known your mom for 3 years...
If its been this way from the get go you have almost nothing you can do but wait.
Cats are odd, every cat is different so there is no 1 way of fixing this. Food/treats are a great start.
It seems to me that this cat just has trust issues. How much time does she spend with your mom? You said you need to keep her locked up, this works but can have negative effects on the cat. The biggest is social issues. ALOT of cats hate being picked up, I know my cat only lets me and my roomie pick her up (he has known her for like 8 years) so you mom may never be able to pick her up.
One thing i would suggest trying, if temping the cat isnt working (food, treats, catnip or toys) try keeping the cat in a differant room then normal... be sure to stay in the room for a bit to make her more at home, then only leave for a bit, work it up so the cat gets use to different parts of the house. As she explores she will get more curious, and hopefully she will get curious about your mom.
Another thing to consider is your moms relationship with cats in general. Some people have a bond with all animals and some people have a "trait" about them that makes dogs/cats/birds or w/e to hate them.
Remember cats live 13+ years so 3 years may seem like it but it isn't that long for a cat, expectantly with the departure of your sister... or any other shock the cat may have experienced in that time.
Just keep trying and trying, one of my girlfriends never got along with my cat. My cat would run away from her or hiss(never bit or scratched)
The weirdest thing about this, my cat LOVES every one... she loves pets or attention of any kind. But in the almost 3 years we dated and the 2 when we lived together they cat HATED her, even though she fed her and gave her treats.
Good Luck.... don't give up!