OK I didn't mean to confuse anyone...A ground is a return path to the source.....so your running lights grounded to the trailer frame, powered by the car/truck will not work until the trailer is hooked up to the hitch...completing the circuit back to the source which is the car/truck.....now your trailer dome lights hooked to the frame is ok as long as there is a complete path...from the battery to a fuse, to a switch, to the light, back to the battery through ground. so the negative lead on the trailer battery needs to be grounded to the frame. as well as the return wire from the light.
I have seen numeriuous times on aircraft where AC grounded with DC causes problems...but You don't have that problem as you're only dealing with DC