Who knows why your daughter is opting for five days in a nursery. We have no idea what sort of person you are nor do we know what sort of person your daughter is.
Maybe you were an amazing mother, and now a loving doting grandparent who wants time with her grandchild. Which is so very valuable to a child - it's such a special bond for a child to have. Yet your daughter wants to prevent it, why? Maybe because she's controlling and unpleasant?
Or maybe you are controlling, and your daughter is trying to minimise the amount of input you over her life now? It can be very damaging having a controlling manipulative mother - and so very hard to break yourself away from that contriol, even as an adult. Maybe she's been strong enough to say no to you getting three days' control over her own daughter, but still feels obliged to let you have your way, so offered you some time on the days you wanted your granddaughter.
Your "it's my way or the highway" attitude and what you're writing in your follow up posts, makes me feel things are more in the region of the second scenario.
Also the fact you wrote this:
"My grandson did often seek comfort from me over mum (other daughter) and she has said she doesn’t want that but I think that’s a little sad, it’s not a bad thing for her to find comfort in me if that was the case."
feels telling. Do you really want your grandchildren to want you more than they want their mothers? I mean it's certainly invaluable for a child to find a granny hug warm and comforting, but having a granny who wants a grandchild to need her more than they need their own mother? That's not good for the child.
One to one care can be better for small children, but it really does depend who's giving it.