My parents look after my DD 1 / 2 days a week whilst I work part time. We have had this arrangement for 7 years now, and as my youngest is starting school, it is coming to an end and my mother is really upset about it.
My children went to grandparents as well as nursery / childminders and it has worked brilliantly for us. It has given the children an exceptionally close relationship with their grandparents - my parents are a part of their lives, they know their friends, listen to their worries, share their excitement when they get a certificate from school or whatever - they have that because they are there, in my children's lives. Furthermore, because my children spend time with my parents alone, they have developed interests together that they enjoy doing, that I am not a part of. For example, my youngest loves gardening with my father and he has been teaching her about different plants and animals etc in the garden. When he looks after her, they go off and tend the plants in the greenhouse etc. They would not have this relationship if they only visited each other as part of a big family visit once a week. They have developed their own relationships / interests with my grandparents that is entirely independent of my relationship with them. In contrast my children's other grandparents (and their maternal great grandparents) are just visitors in my children's lives and whilst my children love them, the relationship is not the same as they just don't have that intimacy.
We have never had rows / power struggles. I have told my mum the rules that are important to me, and the ones I would like her to maintain. She respects that. In other respects, she parents differently to me and I respect that too.
However, for us it is more than just 'free childcare' as we are indeed very close. We live close geographically, but also my mother was there at the birth of both of my children, we holiday with my parents every year, have meals out together, quite often my parents will pop over of a sunday evening and we'll go for a walk / drink together. That sort of thing. That said, before children we did use to socialise with my parents too. (We do have lots of other friends, before I make myself sound really sad!). But actually, my parents have crossed the boundaries into just people I enjoy spending time with now and I think that is reflected in the way my parents just enjoy spending time with my children and sharing in their lives.
And yes, I do hope sincerely one day that I too will have the opportunity to look after my grandchildren in the same way. I find it interesting that my Grandparents looked after my cousins whilst my aunt worked, but she never looked after me, as my mum was a SAHM. My grandmother has this same intimate relationship with my cousins that she never developed with me. She is a part of my cousins' lives, she knows their friends - they stop and chat to her in Tescos still! Whereas she wouldn't know the names of my childhood friends. I love my grandparents dearly, but she was only ever a visitor on my life, and I have never had that intimate relationship that I see in my grandparents / cousins and parents / children.
Sorry, this is such a long thread, but I do believe that when a grandparent looks after a child it does create a very different dynamic in the relationship, one that can be impossible to describe - but in my experience, it is very real!