If you want to delete a personal book, you have to delete the entry in the personal book pane, and restart. That works fine. But on other laptops that sync, the entry is removed from the personal book pane, but the resource exists still in the library - so over time you might have numerous resources in one library and not in another. This affects indexing, searches, etc., and the only way to resolve is to manually hide/unhide the resource on each computer.
Also - if you upload resources to Personal Book, there is no way to delete them from Faithlife server.