You are asking the right question. I think you keep rerunning the stories about your younger self to show yourself that there are at least two ways to move beyond a mistake: You can confess, make retribution and move on. Or you can justify a theft and continue to feel smug that you pulled something over on someone you are angry at (in this case, your mother).
This is not to say that your mother is right to be more supportive of your sister than she is of you. But, at 31 years old, isn’t it time you gave up trying to make her love you the way you want her to? Either she will or she won’t. Exacting some sense of revenge by repeatedly reminding yourself that you once got away with stealing $60 from her seems pointless, doesn’t it?
You are not going to change your mother. You might be able to change your relationship by dropping your end of this fight. Maybe so. Maybe not. But in the meantime, you could love yourself better by focusing on maintaining relationships with people who do love you. Continue to be a good friend to your friends, a loving partner to your husband, and a nurturing mom. Those are the relationships that count now – far more than the thorny relationship you have with your mother.
I wish you well.