How to deal with bad department chair?
This question looks a little bit opinion based, so it may actually be forbidden to ask it here, but I try my best..

I would advise you to really think again about your assumption "'I'd win' for sure". I don't know your situation, but I cannot believe it's so sure due to many reasons:


Often, if it is too late, new courses can not be added even if there was some mistake before. This is due to many reasons: room booking systems, maximal amount of hours professors want/are allowed to teach, administrative reasons, reasons related to budget etc.
Why should a new course be added if only you want to take it? If others want to take it too, why did it not have been added?
The statement "I'll be an unhappy student" comes across a whining even if it's true and is probably not convincing.
This chair seems to have a lot of influence and, if you are correct, acts in bad spirit against you. How do you know she/he will not continue to tell their version of the story to the Vice President? Normally, the voice of a student will not be heard in academia.
The whole issue sounds to irrelevant for a Vice President to take on.


From your story, I do understand that you are in a small college (this chair knows you so well that they even act against you) and the chair would be willing to act against you and your sister. From this viewpoint, I would advise you against doing something.

Sadly, in my experience, professors often get away with bad behaviour and students are often not considered. (This may be different in other places.)

Try to get happy with the other courses and study your subject on your own. Good luck!