Should I let my sister know if our mother pes on?

My sister has held a grudge against our Mother for 45 years, she has cussed our mom out, calls me names, and acts like she is a queen to her kids and husband...The Question is this....Our mother is very elderly, I am her caregiver, my sister has never helped, even though she lives close enough to, she used to call my other sister names, laugh at her, and my older sister was the caregiver to our mother, My older sister died from brain cancer. My younger who is alive never visits my mom, never sends her anything for Christmas, her kids, my mother's grandchildren never visit her or call her, why I don't know, she has been good to them, I guess my sister turned her kids away from her to, should I even let my sister know? She doesn't deserve to attend my mother's funeral even though it would be her mother, and she will never know unless I tell her, she never talks to our mother anymore or for that matter, me either, My son and DIL and granddaughter visit her, call her, help out...but that is her only grandson that does, the 3 sons of my sister never call or visit her either. I say no...What is anyone's opinion?