I don't know if reason can settle this argument. Ego and pride seems to be a strong element. People who go behind your back to get their point across are playing unfairly, and don't care what Webster has to say. I hope you will be able to resolve this civilly. But I have my doubts about that. You could make a poster or hand outs with Webster's explanation of both words, with examples of each samples. I would draw boundaries of how we will proceed, allowing for each to teach their method without being put down by comments from the other. And when talking to shop owners it will be together so no confusion or misunderstanding can occur. If this isnt accepted by her, then she is dishonest. Break ties.