When my own children were younger, one of the most annoying terms of address to me was to call me 'So and So's Mum'. I was always very insistent that people addressed me by my name.
My first child was born five years after we married, and we had been trying from six months after the wedding. It was heartbreaking when people kept asking me 'when are you going to have a baby?'
I would NEVER ever do that to anyone else.
As for g.children - I was not that keen on having these. I adored my adult children, found it difficult to lose status with them to become second in their lives when they got together with partners, so was not enthusiastic about moving even further down the line with their children.
Four of them did go along and have children. I have never been one of those people who think that being a g.parent is the greatest thing ever. My great joy was in having my own children - nothing can ever displace that. As my g.children make my children happy - then my bubble of love extends over them. I join my AC in the celebration of g.chldren achievements, etc. but all my AC know that when I visit I visit THEM, not their children.
Fortunately, my family tend to have children quite late, so I may be still around when the first GG children arrive, but probably not and this is not something I am looking forward to.
Some of my friends have g.children, others do not. Conversations are not about them, it is about us. I rarely mention mine when I am with any of them, and NEVER pass round baby pictures to anyone.