You have dealt with this person before, you can probably play the situation out in your head, you know exactly what they are going do -- so decide what you are going to do. Decide beforehand what you want to do and stick to that.
Control Your Reaction
A person who doesn't care has a tremendous power. If someone upsets you because of what they believe, ask yourself "Why do I care?" You can't change or control people, but you can control how you react to them.
Don't Get on Their Emotional Bus
Stressful people will try to take you on an emotional ride with them. They get angry, you get angry and yelling happens. They get sad, you get sad and everybody's sad. Don't get on their emotional bus. Listen, talk, communicate -- but don't let them control you by triggering negative emotions.
Know What You Need
When meeting with a stressful person, know beforehand what you need from the meeting. What are your goals? Keep those in mind as the conversation ebbs and flows. Bring the talk back to your goals. If you can get your goals met you have learned how to deal with this person.
After your encounter with the stressful, don't keep thinking about it. If things went badly, move on with your life. You can be sure the stressful person isn't thinking about you. Don't ruin the rest of your day. Create a plan for next time you are in that situation and let it go.