exoticfruits - i agree with you when you say that
"I think that it is merely to safeguard the rights of the thousands of lovely people who are perfectly normal but, throught no fault of their own, are cut off from their grandchildren"
of course if the parents split up then the maternal/paternal grandparents should be entitled to still have contact with their grandchild, providing that they were part of the grandchild's life before. it's heartbreaking if they are suddenly cast aside and cut off from their grandchild's life. i do think though, it should be on the father/mother's own time that they arrange for their parents to see their child.
i don't agree with
"It has always struck me that as a mother, when mine were little, I had way too much power"
if you felt that way then fair enough, but i think you had the right to that power, you grew that child, carried that child and gave life to that child. you had every right to that power. of course that doesn't mean that dad's shouldn't have that power either, i just feel that in most cases the mother is the main carer and knows what's best for her child, usually more so than the father, so if the worst happens and parent's separate, mother's should still be able to retain the "power" as you call it.