The fact that the cardholder authorized a family member to use the access device does not negate Reg E protections if the card was stolen from that family member.
If your investigation concludes that the family member was lying and actually did perform the transactions, then you can deny the claim according to the definition of unauthorized EFT in 1005.2(m). However, in order to reach this conclusion, the family member would have to admit to lying or you will need evidence from the merchant(s) which may mean obtaining video surveillance there are no chargeback rights for in-person purchases.
_________________________
Sola Gratia, Sola Fides, Sola Scriptura, Solus Christus, Soli Deo Gloria!
www.tcaregs.com