What is interesting about Ray Bradbury's choice to call the children's room their "nursery" rather than their playroom or something else is that "nursery" is a word which is typically associated with infants or very young children. Such young children, babies even, are very much associated with innocence. In the story of Peter Pan, for which George and Lydia Hadley's children—Peter and Wendy—seem to be named, the children still have a nursery, though Wendy's father believes it is now time for her to move into her own room. Wendy rails against this proposed change, not wanting to leave the nursery.
Peter and Wendy Hadley, on the other hand, seem to have already completely lost their innocence and ought to have been removed from the "nursery" long ago. The fact that this word is still used is terribly and awfully ironic, given the fact that Peter and Wendy, when not getting their way, plot to kill their parents in a horrifyingly brutal manner. When their parents discuss keeping the children from the nursery, as Mr. Darling does with Wendy in Peter Pan, these children actually plan their parents' demise, a comment on what being spoiled does to children's characters. George Hadley has said that "nothing's too good for our children," and now they have become entitled and cruel.