No competitive grandmothering in this family. The other grandma was there for the birth, she is DDil's mother, and we went up once the birth had happened. DDil's mother lives a few miles away, we live 200 miles away.
We have both crafted entirely different styles of grandparenting that suit us and our circumstances. Our families are so close we stay with the other grandmother when we visit and she comes to stay with us and both of us speak of the other as 'family' and share all family occasions.
I always feel very sorry for those people whose only interest in life is their grandchildren. I feel in many ways they are cruising for a bruising, family break-up, grandchildren growing up and so many other events can lead to the collapse of what is an inherently fragile relationship and they are then left utterly devastated with nothing in her lives.
Grandchildren should be part of our lives, not all of our lives.