The whole concept of Police Officers wearing uniforms while working for somebody or something not their agency has always seemed to me to be a bad idea. If he does something wrong and gets sued, the City and Department and the employer all get sued. Why should the City and Department get involved? It almost appears to be asking for trouble. That little phrase "Under color of authority." comes to mind If you're not representing the city, I don't think you should be wearing the uniform.
I think the Chief is well within his rights to order you around. IF YOU ARE WEARING THE UNIFORM OF HIS DEPARTMENT, GIVING THE APPEARANCE OF BEING AN ON DUTY OFFICER THEN THE HAMMER WILL FALL ON HIM FOR ANY PROBLEMS. If you really need real Police presence, then contract it through the City by paying all the costs.
Consider this scenario, a disturbance a brawl , you might make normally make an arrest or two, but have to call for back-up or somebody else calls, on-duty officers arrive, a Supervisor comes to the scene. Who is in charge, the guy you working for or the on-duty supervisor, what if the on-duty Supervisor realizes a crime has in fact ben committed and there are sufficient grounds (under your state laws) to make an arrest of several participants . One guy is your temporary boss, or his brother or his good buddy or his wife who was wearing YOUR badge on her sleeve while boozed up and your temporary boss doesn't want him hooked up and hauled away for any of several reasons. The Supervisor says bullshit, they all go. WTF do you do then???