The facilitator gradually steers them into a dialogue. During the exchange the facilitator needs to be prepared to stay out of the way, letting the process flow, but ready to intervene when it isn't flowing. The goal here is for these two people to talk honestly and constructively to each other. So long as that is happening, the facilitator's guidance is minimal. Here is a catalog of third-party interventions that the facilitator may make during the course of one or more meetings with person who are on conflict and need to manage it more effectively.
Individuals publish to each other what they imagine about the other.
Making a chart of the opposing forces in the situation, those pushing toward change and those resisting. I assume that you know. Participants take turns testing whether the other knows something that the speaker assumes that he or she knows. Individuals share with each other their scores on self-assessment instruments in order to build understanding. They take turns on the bad news lists, paraphrasing, until they achieve a sense of closure.