Ken,
So for this exercise, no AC shore connection, and the charger inverter is off before you start wiring. Basically we are taking the transfer switch out of the equation by jumpering these leads. Individually each hot lead from the genset gets connected directly to each hot going to the coaches AC power panel. The neutral from the genset gets connected to the neutral wire from the power panel. The grounds can stay as they are given they are bonded and do not get switched by the transfer switch. So three wires individually are connected from the genset to the AC power panel input wires.
You would then want to turn off the main AC breaker and start the genset, let it run 30 seconds, and then if all is well turn on the main breaker and monitor the voltage using the coach systems and vary the load by adding and removing AC items in the coach. When you are sure it is working well you would then turn off the main AC breaker and wait several minutes and then shut off the genset. You can repeat this process over several days as many times as need be until you are absolutely sure the genset is or is not the source of the issue. Once you know the problem source you can work with the transfer switch people or the Onan folks if need be. Safety first on this, double check the wiring before you fire up the genset and make sure you have the wires labeled or diagramed so they go back as they were. Hope this helps and safety first...
Later Ed