This issue will depend on who was an authorized user of the credit cards. If you sister and your deceased mother were the authorized users, then the responsibility would fall on your sister. Based on your information, it would be up to you and your brother whether you would want to help your sister.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyze this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here
The responsible party is the party that took out the credit card. Authorized users are not responsible on a credit card meaning....neither yourself or your sister are responsible. If it was only your mom's credit card then only your mom would have been responsible. Advise the debt collectors that if they keep calling and harassing you that you will bring an FDCPA claim against them as this is not your debt and you have informed them of such.
Your mother's estate is liable for her debts. You and your brother are not liable. Your sister may have to pay for the accounts that were joint with your mother. Advise your sister to see a consumer attorney who handles debt collection cases. She can look for one at naca.net.
The answer given is for informational purposes only and does not constitute legal advice. Dwight Bowen is a bankruptcy and consumer attorney and may be contacted at (404) 880-3310.