Maybe ask the admin specifically for some examples of the problems that require your intervention, and how they interpret that. What particularly bothers them?
Also, I think you could take a year to assess things before you begin to change things up.
Surely your own classroom and how you demonstrate inquiry-based education will speak loudly at first. It would cause others to stop and think, perhaps, so you didn't need to speak. Waiting a year might earn you the right to be heard, as you gain relationships with the instructors themselves.
As you wait you could offer ways the teachers can see what you are doing and why in terms of your teaching. An art show, a video, a workshop, a handout, an open house...??