The other issue concerns the center's liability. Signing a confidentiality/non-disclosure agreement may not give them enough peace of mind.
You could sign the agreement and violate it anyway. Because the center can't prevent third parties from suing, they may demand an opportunity to review your manuscript to ensure that you don't, in fact, disclose any client confidences of intellectual property of the center.
They may also want you to procure your own insurance to cover any liability for these outside business activities. In either event, speak to an attorney in your area who is familiar with publishing law and liability to make sure you steer clear of these thorny areas.
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.