Facts will always be on your side.
Were I you, I would make darned sure of what the processes currently do, and how they are done, in order that you can confidently state How It Works Now, and hopefully be able to get to "How It Should Work."
Try to ignore the drama and dedicate yourself to the business at hand. Take a deep breath and dive in, documenting the crap out of it.
You cannot control anyone, you can only control how you react to them, so stay on the side of professional business and you should be fine.
If that all fails, just remember that you were looking for a job when you found that one. You have marketable skills and it is your choice as to where to utilize them. Hopefully it won't come to that, but there are difficult people in the world. Some are worth working with, others are not.