Emotions are not your friend when they rule your interactions with your difficult person. You need to be black and white, focused on the facts, calm, cool and collected. You will have no problem dealing with issues that you are not emotional about (because you don’t care), but as soon as you “care” you will have a problem dealing with the situation.
It is in your best interest to NOT respond nor react when you are being ruled by your emotions.
Take time out. Be sure to arrange a follow up with your difficult person when you can get some perspective, when you can be calm, focused and professional.
You are emotional for a reason. Are you being ruled by fear? What are you afraid of? If so, figure out what is at the root of that fear, and see what you can do to work around it (are you afraid you’ll lose your job, the boss won’t like you, that you’ll look stupid?). Your fear will probably not be rational. But once you can identify the fear, then you can deal with it.
Your emotions will be easier to handle when there is understanding.
So, what are you afraid of?