I have created a home user account for my wife. She has one library shared with her that only has media she will watch. I would like to have the ability to let her delete from this library. Is this possible.
No. Plex made a decision to not modify your files in any way. The only exceptions to that are that the server owner/administrator can delete media files, if that option is enabled. The second exception, apparently, is that the Plex DVR, currently in beta, has some ability to delete watched shows.