Are you saying that you hook up the city water connection, turn it on and all is well - and then you turn on the pump and get water dripping down the outside of the trailer, at the city water hose connection? I don't think this is what you mean, but if so, my first question is why do you turn on the pump?
More likely you mean that you do not hook up the city water hose. Instead, you put water in the TM's fresh water storage tank, turn on the pump, and then see water drooling down the outside of the trailer, coming from the city water hose connection. In this case, the picture at
https://www.trailmanorowners.com/for...&pictureid=435
suggests that the pump is producing pressure as it should, and the fault is at the one-way valve at the city water connection. Fortunately, I believe that the city water hose connection, including the one way valve, is available as a single assembly. Check one of the RV parts supply places like Dyers Online, PPL Motor Homes, or Etrailer. The whole assembly should pull straight out through the wall of the trailer, but if there is not enough slack or movement in the pipe from the assembly into the trailer, installation may be tougher simply for lack of access.
Before you do this, I think it is worth hooking up a city water hose and running a few quarts through the fitting and into the trailer - just drain it into the gray water tank or out on the ground. If there is a small piece of crud in the one-way valve, this will dislodge it.
Bill