You know, I've had friends with this problem and what was driving it was the grandparent. THe grandparent who was jealous of the kids' time, wanting to not disrupt her own schedule (despite that if she were REALLY a daycare, the parents would be allowed to pickup at ANY time of the day they chose). The grandparent didn't think of it as providing daycare but rather her own parenting time with the kids...
And it got worse when the grandparent heard only her child's point of view about the divorce & new life of the other parent, and took sides & such. And if I remember (it was several years ago), the grandparent ended up funding her child's attorney to fight on that issue.
In the end, my friend figured it out and worked it out with her ex that his mother needed to BACK OFF... and somehow it happened that the grandma was put in her place.
It's interesting how reading this thread brought that situation to mind, because it was a while ago & I only kind of heard things third or forth hand in that situation ... not like it's at the top of my memory banks, you know? So I thought maybe I should mention it... as a possibility. Just something to think about.
Maybe if it's a remote possibility, it would help to work to get Grandma on board with the plan, rather than springing it on her like you would with a normal daycare facility?