Hi Rebekah thanks for posting in the community! I'm happy to help. Unfortunately it is not possible to restrict viewing permissions (whether via normal sharing or by publishing) at the level of individual layers. In your scenario I believe the most effective way forward will be for you to duplicate the document you want to publish with the secure data visible and publish it as an entirely separate document with its own link. This way you ultimately still have different links that correspond to different levels of access. 

If you'd like to see support in the future for sharing or publishing permissions by individual layer our development team would love to hear more about your use case via this feature request form. Thanks for your feedback and apologies for any inconvenience. Please let me know if you have additional questions!