The younger brother at home is very ignorant and always scolds the old man. I can't stand telling my mom that I don't have to educate her. I am really angry.

A person like your mother thinks she is an elder, and she won't listen to anything you say, because she feels embarrassed that her children say their parents are wrong. I think you can talk to your father or someone close to your mother about this situation and ask them to persuade your mother. Maybe your mother can still listen, and at the same time, as a sister, you can educate your brother to understand his bad behavior and correct it later.