The witnessing awareness is the most empowered part of your consciousness; it's actually your connection to the creative power of the universe, and once you tune into it, awareness itself will, over time, integrate all the contradictory energies within you. When you tune into the witness, gnarly feelings let go.
That may be enough in itself to shift the energy between you and your difficult person. But if you want to go farther, and use the creative power of consciousness to communicate subtly with the person, or at least change your internal relationship to him or her, you can use symbols, which the unconscious recognizes more easily than words. You can use a practice like Fran's flower meditation. Flowers are a universally recognized symbol of appreciation and reconciliation, but you might also use an olive branch, or another imaginary gift.
I like to do this by imagining myself walking into the heart. A ladder connects my brain to my heart, and with each inhalation and exhalation, I walk myself down that ladder. In the heart, I imagine the two of us sitting in a cave, with a candle between us. Then I speak to the person. I ask that the two of us be friends, or that we be at peace. Sometimes I say what's bothering me in the relationship and ask for help in resolving it. Often, though, I just imagine us sitting together in the heart space.
Once I've done this internal process, I find the confrontations I've been dreading turn into reasonable discussions.
The creative consciousness of the Great Mind is best contacted through the heart. When you use active imagination, or bhavana, to resolve a relationship inside your heart, you are putting this insight into action. I've long suspected this is how the difficult people in your life can become your teachers—by inspiring you to change the dynamics of your relationship with others by shifting the dynamic within yourself.