The physical environment of this particular mediation would have to be well thought out and secure to ensure no violence will erupt. I would certainly begin by silently arranging the mediation at an open facility near a police station or some other type of assistance should something happen to go south. This of course would not be known by the participants as a deliberate pick, but would certainly be in the decision. The parties would be strategically placed far enough from one another to discourage and avoid physical contact but close enough to speak comfortably. I would also alert the local authorities to the mediation taking place so they can be on alert in case something should happen. With adults, so long as they remain professional and acting as adults, should be able to have a heated, but orderly mediation.
Do you feel that having on-site security would be a problem for the mediation? Explain.