On the trailer there is no load on the engine and no back pressure on the exhaust, first do a compression check and check for fuel to all cylinders and for spark to all cylinders. Spark plug color will tell you a lot about the engine also. SILVER, GREY, WHITE, BROWN, BLACK all mean something different is going on inside the combustion chamber.
Most weak or messed up engines sound good out of the water. On the pump issue also check for clearance between the edge of the impeller and the liner excess wear will cause serious cavitation.