*Well I would assume the nursery and its staff are paid to take the children that morning?
Also assume the library story time is free?
On that basis I would be miffed too!!*
I don't understand this post. Why does it matter if the staff are paid (of course they will be - they are at work, looking after the children)?
I'm also not sure why it's relevant that the nursery is private. There aren't many state ones, unless a lot has changed recently, and even if there were, anyone has a right to use public services.
The problem is the rule about numbers, and the fact that the library staff allowed so many nursery children in at once. Could you ask to speak to the librarian, if there is one?
Nowadays, a lot of libraries are staffed by untrained volunteers, so I'm not surprised that there are 'incidents'. This is said with no disrespect to those who volunteer, as without them many libraries would close, but it took years to train as a qualified librarian, and the role can't be filled properly by someone with no training at all. It is also a shame that so many well-qualified people can't find jobs, as it is assumed that anyone can do it, and do it for free.
In some ways, that is beside the point, although I suspect that it underlies your problem. Even if there is no librarian on the premises, someone must be in charge, so I would ask them if there is a way you can 'book' ahead, so that you don't waste your journey and disappoint your grandchildren.