Oh what a difficult situation and I sincerely hope you manage to all come to some sort of an agreement that works for everyone, but most importantly you maintain regular contact with your grandchildren. The role of a grandparent is to be a link between children and parents, telling them stories about their mummy and daddy when they were young, being able to play and enjoy the grandchildren without the pressure that they had when they were parents themselves, trying to juggle lots of balls in the air, ( and in my case usually failing miserably) In other words, be part of their lives, their history ! All too soon they grow up and are busy at Uni or whatever but its good if there has been a special bond created when they were younger.
I have two grandchildren, whom I see every other week, because I look after them one day a week. On the weeks the other grandparents step in, I arrange a day to suit my daughter when we can come and simply be grandparents/parents rather than childminders.
I genuinely hope this all works out for you, I have a sneaking suspicion and I hope I'm wrong but your daughter and son in law is between a rock and a hard place, and if this nanny is otherwise perfect and allows her and her husband to work with peace of mind and come home to a well organised household, then be prepared for conflict of interest and the need for compromise, However, it has to be discussed and its imperative for you all to be able to move forward in a way that suits everyone. Mention some of the excellent suggestions from other posters here would be a good starting point .
On a lighter note, I wonder does Carol Middleton have this kind of problem ?