Assuming there is an external person arbitrating (which is usually the case when dealing with internal politics at least -- one or two levels up from you), it's so important in these cases to stay reasonable. Virtually every single time, the person that likes to fight will cross the line in the hopes of goading you into a fight. But it's exactly at that time that you win. You send a very reasonable email to the arbitrating person saying, "I'm really trying my best to get this working, but I'm having trouble. Could you please give me a hand." Since the arbitrating person really would rather do nothing, they will look at the situation and say, "A is completely reasonable. B is not. B, you need to change."

I remember one time where I was discussing a problem with a manager in another team. Every single email he sent, he CC'd the management 2 levels up. Every single email I sent, I sent directly to him only. My colleague was panicking. He felt that I needed to show my side of the story to upper management or else I would be in trouble.

Eventually the management 2 levels up got frustrated: "Why am I getting all of these emails? Why can't you people sort out this problem yourself?" To which I reasonably replied, "I'm very sorry that you've been bothered, and I'm not sure why this person is being so difficult. Now that you are here, would you mind giving us a hand?" Problem solved.