What does it mean to be a signer on a checking account, but not a partner in the account?

apparently my sister did some rearranging with my dimensia affected mother in our trust account and had her sign some papers. Our new checks came back without my name on them and they no longer had my mom's name as the trust account holder. They just have their names on them. My sis told my mom that they just forgot to put my name on the checks but i could still sign and not to worry. The guy at the bank said not true. If my mom dies, my sis gets all the money now. The will is no longer valid that says we split the money and the trust is null and void. And, if they both die, the account goes to probate. True? He said i am what is called a " signer'. My mom is so out of it, she thinks i''m lying. She trusts my sister so much. And since this has occured my sis has been trying to put my mom in a home. I' ve been scurrying arround to psychiatrists that will say she is fine to keep her out of one. My sis has made some very bad financial decisions and is deeply in debt. What is the truth about the account?