Unless you are having the Christmas celebration, nothing you do/say can invite your Dad anywhere (other than where you are inviting). If your sister is having the party, you're not in control, she is. Sounds like your sister is confused about who is in "control" of whom and that she wishes she could be in charge of the other adults. As you say, I don't think your dad's girlfriend is going to want to come to such an unwelcoming place.

I would try to talk to your sister about what kind of person she wants to be; a gracious hostess or a "shrew" :-) It's not about what your Dad or Mom or the other adults do or do not do but about what she chooses to do that determine how she will "turn out" as a woman. Holding a grudge is about her issues, not theirs and doesn't hurt them. You have already wisely seen that your dad's girlfriend is not someone you want to know much because she made no effort to get to know you. I think that's wonderful that you at least made the effort to find out.