by Randy Carey: The card was stolen and the transactions are unauthorized.
by Jim Bedsole: Reg E does not provide any relief to the bank even where the customer has been negligent. Even if the mother wrote the PIN on the card itself and left the card in plain sight, the fact that it was taken and used without the mother's permission makes it an unauthorized transaction subject to Reg E reimbursement. If the unauthorized use was reported in a timely manner, the maximum liability the bank can assign to the mother is $50 (this may be $0 if Visa/MC rules apply).
by John Burnett: Let's back up a bit. Start by nailing down who made the transaction in question. It was either the daughter, who had permission to use the card, or it was someone else. If you come to the conclusion that it was someone other than the daughter (such as her friend), and the daughter wasn't involved in the transaction, it's not authorized and you have to treat it as such. But if the daughter actually completed the transaction, the transaction was authorized.