I don't want to visit my dying grandmother even though she wants me to.
Do you have a reason for not visiting her grandmother?
I don't care for old people at all
I don't think visiting a family member on their death bed is about caring or not.  It's about showing respect, and you should always pay your respects to a family member when they're dying.  You don't want to be alone when you die do you?
I'll be too busy shopping.
The rest of your family is going to think you're cruel and it will strain your relationship. Even if you don't care for her you should at least see your dying grandmother, especially since it sounds like this is the last chance you will get to see her.