Where I cam from, for example, a MVA, the Sheriff/State Partol took care of the traffic. The Rescue Squad handled the extrication, and helped with treatment and the Fire Department made sure our scene was kept safe for us to work in. Sure, there was sometimes cross role's being done. But the main thing was the safety of us and the patient(s).
We came to this great relationship by getting together and having cross training. Regularly! And another way is to do joint community events with all agencies. ea: community bbq's..community health and safety day. Have members of the different departments dig in your rig and play with your stuff. One day, or one night at 3am, someone on the other department might remember where you kept that short backboard when you need it because your holding your patiens cervical collar and your *ss is stuck in the smelly wreak.
Its all about communicating and sorting differences...at the station..not the field.
rock on!