See
I am getting errors with my calibre library on a networked drive/NAS? for the FAQ entry.
Did you go into the Google Drive Backup and Sync (should be located in the system tray). Open preferences, select sync only these folders, add the folders you want synced, exclude the ones you don't want synced.
To move your library, close calibre and copy your library to a new unbacked up location. Open calibre, and under the library drop down menu, open Switch/create library. Browse to your new library location, make sure the Use the previously existing library at the new location radio button is selected and click okay. Check the library and all looks good, you can remove the old library.
I prefer this to allowing calibre to move the library.