Yes you do have a restriction. Any time the initial flow is high and then drops off that is a classic indication of a restriction.
Not sure what year your trailer is but if it is old enough to have copper pipe I would look for a bent pipe that has almost collapsed. If the problem is only on the hot water side I would look at the connections at the rear of the heater for a build up of calcium across the pipe. If it effects both hot and cold you are just going to have to cut into the system at different points until you are past the restriction and replace some piping. There is most likely some foreign matter in there.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles