We took ours to a Cummins location and they found the problem with our Onan generator right away. They found a hole in the fuel line to the generator. The manufacturer used the wrong type of hose. Fixed it quickly and reasonable price.
Have you ran this combo before? Just a guess here but did you start them in that order? The A/C will draw a bunch of power when you start it up then it will need less voltage when running. Someone was mentioning last week how much it takes for a coffee maker to run off his inverter, I was surprised.
If, indeed "not enough power" is the problem, as with any diesel the first two things to check are fuel and air.
Fuel filter should be changed. Have also seen a number of air leaks into the fuel system (bad seals on filter, loose fitting, cracks in fuel line from tank, too low a fuel level in the tank).
Air is the other thing your diesel needs-- check condition of air filter.