Evolution of time marches on, but some things do not change, like the face of a child searching the audience for a parent's face and then when they find them - that moment of relief and then pride. You notice them lean over to a friend and then point you out only this time you're there as a grandma watching the next generation and it still feels wonderful.
And the hug afterwards when you tell them how wonderful they were and how proud you are, the glow and the beaming smile are your reward. And then later you go back in time remembering and reminisce with your own child and the pride is a recognition of your own and they are remembering too.
You share a bond at that time and it's good to be included. This is family, this is love, this is what life is all about, to love one another.