What term is used when Mary attempts to support her father's role and create distance from her mother's complaints?

The term "detriangulate" accurately describes Mary's behavior in the scenario, where she supports her father's role and tries to create distance from her mother's complaints. Detriangulation refers to the process of changing the dynamics within a family system, specifically removing oneself from a triangular relationship where one person may become enmeshed in the conflict or emotional issues of two others. By supporting her father, Mary is working to stabilize the family dynamic and prevent the conflict from involving her as a participant, thus fostering healthier interactions.

Detriangulation is essential in family therapy as it helps individuals to take a step back from the emotional turmoil and enables clearer communication between family members. In this case, Mary's action helps her father feel supported while also keeping her mother from pulling her into an alliance that might perpetuate conflict.

The other options, while they may relate to family interactions in other contexts, do not specifically capture the essence of what Mary is doing. Reconciliation involves coming to terms with past conflicts, compromise suggests finding a middle ground, and empathizing refers to understanding another's feelings—all of which do not precisely define the act of supporting one parent's position while distancing from the complaints of the other.