What is it called (Preferably single word) for phenomenon that is taking place when three parties are involved such that first two persons (Group of people, party or Departments, etc) are at not good terms with each other. And so first party involves you (or your department) as the third person to talk (Converse, correspond) to the second party and vice versa. The question is about what kind of phenomenon is happening between all the three parties and not what the third party party is doing individualistically.
The point of this is to highlight to the management the amount of work that the third party (its department or members of its group) have to undertake is a overburdening our department (third party).
Example: ________ is causing excessive work burnout, disgruntlement, disengagement in our department (within third party) since the XYZ department (first party) is reluctant to correspond with ABC department (Second party) and vice versa. And we (third party) have to pay the price.