Could you please clarify whether you are all in North Carolina? When you refer to the courthouse, are you referring to a courthouse in California or in North Carolina? Which courthouse is your mother's estate being probated?
Your question was posted in Orange, California; but your question ends with you stating that you live in North Carolina. You need to bring a challenge in the same Probate Court where your sister opened the case; bringing a case to remove her as executor, including a demand for an accounting, and asking the court to re-open the Probate so that all of the heirs are included and notified. It is unclear to me in the facts as presented where the Probate case took place. You should obtain legal counsel from an attorney who handles "contested probate" cases. Without more information, it is difficult to provide any more response.