Let me add this datapoint here. I dint know if its been mentioned before (bcos this thread is thicker than a holy book) but if you add a card and the cardholder name you enter doesnt match the one you have listed in the Amazon account it will not be selectable from the dropdown box when selecting the card you want to send to.

Real example:

I add a few cards (GCs) at a time and in order to distinguish from them i will put some identifier in the name field along with my last name. For instance, instead of John Doe for my name i would put STAPLES Doe. Staples being where i got the GC from. Well if you do that then the card isnt listed in your dropdown for payment card choices.

Changing the card holder name to JOHN DOE enables it. This isnt a hard and fast rule as i have had cards selectable with things like AMEX DOE in the name field.

The take way is they may not let you use your family members card (as long as you list the card holder as anyone else but you).