Should I sell this horse or give him a chance?

This is pretty typical of a older lesson horse. Since they haven't had too many good riders they pick up really bad habits. I would probably sell because a) you have a buyer b) your mom doesn't want to actually ride THIS horse c) you don't like him and d) I'm guessing you already have your own horse. Why spend time and energy working with a horse that doesn't have too much potential to start off with, especially one that isn't yours?