“Who steals my purse steals trash. But he that filches from me my good name robs me of that which not enriches him and makes me poor indeed.” This quote from “Othello” begins “My Reputation,” and it is a strong reminder of how our conduct, even if well-intentioned, can affect others. Jessica Drummond (Barbara Stanwyck) has just lost her husband. They had two sons together, who are now 12 and 14. Family lawyer Frank Everett (Warner Anderson) is a good friend and real comfort during this difficult time, but Jessica’s mother, Mrs. Kimball (Lucile Watson), on the other hand, just wants to tell her what to do. Kimball seems more concerned about following conventions than about her daughter’s happiness. When Jess’s sons go to boarding school, she becomes terribly lonely. Her friend Ginna (Eve Arden) invites her to spend the winter at a cabin with her and her husband (John …