Thank you for the setting check. Tried it but that didn't help in our situation. We eventually had to make sure every DEVICE was authorized in BOOKS (in the Account) and found we still had long discarded equipment that was taking up space. Got rid of those and insured current devices were "Authorized". Then the Originator deleted me from Family. When the Family was renewed with both of us included, I could see the book in the "Recent" option (upper right 3 dot (...) dropdown) and was allowed to download it instead of only told I "Cannot Redownload without purchasing". No idea where the Family programming thought I'd already downloaded it or that this iPad wasn't in the Family. Those old Devices also seemed to impact Family sharing in Music.