My first reaction to this question is whether or not the grandparent and/or the spouse are capable of making decisions for themselves. Many elderly people are. Only some have dementia or Alzheimer's Disease. If the person, him/herself, can decide that's who should decide. If he/she cannot decide then the spouse should decide. I suspect that in most such cases both partners don't have dementia or any other inability to make his/her own decisions. Many times, younger people don't understand that some of the things elderly family members do are not signs of dementia at all.
If both spouses have been diagnosed with dementia then it would seem the next in line to make decisions would/should be their own grown children. If there are no grown left, then, of course, the decision may have to be up to the grandchildren (hopefully, with the advice of more than one expert who knew the person in question very well).
I think, though, that in general nobody should be thinking about "sending" an elderly person to nursing homes unless the person has serious enough dementia to pose a risk to himself AND does not have a spouse capable of making the decision; or unless the person needs round-the-clock nursing care, there is no way to provide that at home, AND the spouse has serious dementia and is incapable of making the decision.