In my situation, UX reports up to me. My relationship with the UX team is a very collaborative one. I generally come in with the problem defined and an opinion as to the solution. My role in these collaboration session is mostly providing thought leadership, asking thought provoking questions, and making decisions as needed to keep us moving forward. Sometimes during these sessions we pin down the experience we want to deliver and other times UX comes back to me at another time with some ideas based on what we had discussed.
In terms of resolving conflicts, the PM is the decision maker and ultimately owns the solution.