Yes I am at a loss too.
It does sound like something that you will need to take it to the dealer to fix it. Sorry.
From what you described, the first thing I would check is the input voltage from shore power to the transfer switch. It seems like from the transfer switch to the RV main panel while the generator is running, everything is normal. So the problem should be between the power cord and the transfer switch input from shore power. It is a short distance.
You might have a loose terminal, or broken wire in the power cord, or plug, or someplace in between. If you have a discolored plug, you can replace that for only about $20 - $35 in parts.
Next thing to check is find the generator transfer switch, and measure the input voltage while plugged in, and output voltage. It should be 110 - 125 volts in and out. There should be less than 1 volt across the input to output terminal. More than 1 volt drop indicates a problem with the transfer switch contacts, and a need to replace the transfer switch.
Then start the generator (with shore cord unplugged) and see if you are getting 105 - 135 volts input and output (again, less than 1 volt across the terminals from input to output). Turn on the A/C unit, and the voltage should drop to something between 110 and 122 VAC. (It can spike when there is no load on the generator to around 125 - 130 volts, 135 is not un-usual.)
Fred.
