What to do with a mean cat

[Bev832]

Hello everyone! Hope you can help.
I joined today because of "Sassy". She's my Granny's cat, and in the past month, she and Granny have moved into my parent's home as Granny is dying quickly. This has never been an affectionate cat, nor a calm one. She is isolated at the moment in one room as there are a dog and cat in the home already.
Granny wants to have Sassy put down because she bites and attacks people, pretty much anytime someone comes near. At this point, Granny would not heal if she bit her. She had started to accept my Mom but has bitten her twice now.
I have an old cat who isn't going to last too many more months, and a year old puppy. We have no kids to worry about. I am more than willing to take this cat in, if there is any hope of rehab. Granny is insistent that she not become a problem.
Can you take a cat who has never been nice and create a tolerable situation? I have always had a cat, but never one with issues. Those have always been reserved for the dogs.
I would appreciate any words of wisdom, this is a really stressful situation all around, and we probably aren't thinking objectively. Thanks in advance,
Bev