I am not a good person to ask advice on this. Because if they were rude to me then I would probably be rude back.
However, with that said, you know that Rosie is beautiful and that is all that matters. When they ask about her tail tell them she is an extra special Yorkie, you know a Yorkie that doesn't have a tail. They are rare and aren't seen very much.
Lol. As far as the rat comment, I don't think I would be able to let that go. I am pretty sure I would have to say something. Maybe like "If you don't have anything nice to say, then don't say anything at all." Good luck to you on this. Hopefully, someone can give you ways to be nice about it. You just remember that Rosie is a sweet, loving, adorable furbaby!