1st time boondocking and could not get our AC to work

A/C starting capacitors wear out. At 10 years, you might need one.
Yes, the batteries charging might be enough to push it over the limit.
What about a water heater......electric ??

Your generator sounds a bit small for the task.

I don't understand your comment about the extension cord.
The main power cord for the trailer should either be plugged into shore power OR into the output plug from the generator.

And finally exactly what happens when the "overload" occurs ? Does it trip a 30 amp breaker ?