To my2sons: You are in a delicate position and your appreciation of the politics here is admirable. I think the key is to get your information to the nurse manager of the nursery without offending the recruiters. You wouldn't want to make enemies within the hospital before you even get the job you want!
Is there any way for you to network with the manager of the unit you are interested in?
For example: Do you know anyone who works in that unit or who knows the manager who could make a discrete inquiry for you? Such a person could say something about "having a friend who is interested, but who was turned away by the recruiters because of a lack of nursery experience... how should my friend go about changing specialties?" etc. etc.
If you have no such friend ... is there a way to meet anyone from the nursery? ... a local professional conference? ... a professional organization? ... etc.
If you can think of no way to establish a connection through a less formal contact, then I would simply write a polite letter to the manager asking for career advice. Seek what career experts call an "informational interview" as opposed to a "job interview
." Your letter should explain you situation and then state that you have learned through the recruiters that the nursery only hires people with previous experience. You are seeking to talk with the manager to learn how you might go about getting the necessary experience to be considered for such a job. If the manager is impressed with you, she might just offer you the job. If she really wants to stick to her guns and only hire peope with previous nursery experience, she will probablly be willing to point you in the right direction to get that experience. Either way, by requesting the "informational interview" rather than the "job interview," you run far less risk of offending the recruiters -- and why make enemies unnecessarily?