I don't believe alcoholism is necessarily the reason for being a mean person. My father was a true tyrant, from yelling to beatings. He didn't drink. But he was raised in a mean home with a father just like him. Often this type of abuse is a cycle.
I was married to an alcoholic who was extremely sweet, thoughtful, and kind. He was gentle, and I don't believe he ever raised his voice even once. He also drank himself drunk nearly every night. He was a sad drunk, but a very stubborn one.
Look to dysfunction in your mother's home growing up, how her parents berated her. There probably lies your answer. The alcohol probably made it worse.