Well, ok, that's my fault for creating confusion. I thought the OP was a medical student looking for a trauma rotation, not a resident (I skimmed), and as such my comment was geared in that direction. Med students can go pretty much anywhere because there's not much in the way of credentialling (which is still pretty minimal for residents when compared to attendings), and temporary licensure. For residents there would still need to be an affiliation agreement between your program and wherever you go, agreements on who will cover the liability, and so forth. And that might take quite a while to get into place.
To the OP: does your program not offer trauma? or is it weak? I guess I'm wondering why you're looking to go elsewhere for that rotation.