I booked a AAA rate for November with CRO. I was curious about rates too and discovered that you can book rooms through our regional AAA website. I just entered our trip information into the site to get an idea of the rates.
Also, I was asked for my card number when I made the reservation. They did not ask me for the name on the card though. So I suspect you could just get the number from your mother's card.
Kristen