I'm not sure on the authorized card holder/joint card holder part, but if you are on the account as a joint card holder, then yes, you are responsible for the entire debt, even if you mom charged all of it. I have a Target Visa, but have never had to add another user, so I don't know how that all works.
And if you are just an authorized card holder, then your mom's estate is responsible for paying the debt. Therefore if you alone inherited everything, you are required to pay the entire debt because it should have come out of her estate before the inheritance was distributed, from what I understand at least.