L.W.
This is part of the nature of learning who you are. They need to be able to resolve conflict by themselves. You can ask them to respect the other's wishes and "what can we do to work together so that everyone can get what they want" Learning to share will probably be easy for them when they know that they are in charge of working out the details.
Check out http://www.emofree.com for a free manual on Emotional Freedom Technique. This is a healing technique that is very good and can be something you do as a surrogate for them when you see tension building to just dissipate the negative feelings.
When they get out of control, have them sit down with both hands over the center of their chest (the area you point to when you say "my name is ______) and breathe until they calm down. As they sit with their hands on the center of their being, have them say, "I want to feel better"
Love, L.