Can my employer gain rights to my book if I sign a non-disclosure agreement?
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.