I was so lucky that my father's parents lived only a few doors away from us. My grandmother wasn't grandmotherly in the typical sense and I don't remember her hugging me, but she had all the time in the world to talk to me and I just treasured that.
When I went to college it was my grandparents who encouraged me to stick with it when I was disappointed. They made a very positive impact on my life and I will always be grateful.
I never met my mother's mother, even though she lived about 10 miles from where I grew up. She and my mother were estranged and they never resolved their issues. When my grandmother died I was in college. I remember standing next to my brother looking into her casket and she was just a stranger, an old woman I never knew.
My mother's sister (M) was also estranged from my grandmother. M's daughter, S, struck up a relationship with our grandmother several years before her death. S used to try to get me to contact our grandmother and my mother even offered to have my uncle take me to see my her but I didn't out of loyalty to my mother. I picked sides.
Lou, BB is being selfish. Your GKs may lose out on a R with her, but they don't have to lose out on a R with you.