I’m so sorry to hear you are ill.
As she goes to nursery, I assume her parents are working. That means weekends are the only time they have hours free together and with their daughter. They have two sets of grandparents to consider, if both sets want to see the child weekly, when do they get a day to just veg out or do stuff together?
Once a week really is quite a lot, do try to enjoy it rather than dwelling on the time you don’t see her. I saw my grandma about three times a year, she always felt like close family and we looked forward to seeing her.
I didn’t sleep over at grandma’s without my mum until I was about 5.
My daughter was about 3 before she slept over at my mum’s without us, she was about 5 before she slept over with her paternal grandparents, - not because they were my in-laws, but because we lived closer to them and further from my parents until she was 5 and then it swapped the other way. She only slept over with either set about once a year. It differs for all families. Often children go through phases of being more or less bothered by being away from mummy and daddy at night.
Please don’t let this blight your relationship with your son, DIL and granddaughter. Guilting people tends to make them pull away.
Seeing her around once a week is a lot more than many grandparents, you must have a lovely relationship!
They are not being unreasonable, it’s just not what you want.
I’m not a grandma yet but may be in the next few years. I am very close to my daughter, but I very much doubt I’d see my grandchild every week as my daughter works long hours in a demanding job and they have good, close friendships to maintain, as well as being close to his parents, sister, Mutti and my ex-husband etc! Life is busy!