Same words, different meanings. You say "Mobile Emergency Response Unit", and I thought "Major Incident Response Vehicle", MIRV for short, of which the FDNY EMS Command has one for each of the five counties comprising New York City. They're kind of Emergency Rooms on wheels, able to take active care of up to 6 patients at a time, with no discrimination between responders and civilians for that care.
On reading further, I then determined you're director of what I know as a "Third Alarm Response" unit, doing true scene rehabilitation of and for responders. We just have coffee, tea and lemonade from the Red Cross or Salvation Army vans, or FDNY "RAC" units (I don't know what the initials stand for).
One of these days, FDNY will, hopefully, activate a field rehab unit, operating much as you've described.
A final thought: WELCOME to the City!