I'd try shutting all of your breakers off and then connecting back to the boatyard's shore power. Does it trip again? If not, turn the main breaker on (leaving the rest off) and see what happens. Then turn them on one at a time until the breaker pops.
I had this happen to me once with my boat's onboard ELCI breaker, the equivalent of the boatyard's GFCI. What caused it in my case was that some rain water leaked into an outside outlet on the flybridge. This conducted enough current between hot and ground to pop the ELCI.
I've also heard of it happening if shore power cables get dropped in the salt water "shaken out" and plugged back in. Eventually it drips in or dries out enough (higher conductivity with higher salt concentration) to conduct enough between the prongs in the inlet to trip the breaker. If the shore power is isolated when the generator is running (as it should be), then shore power shouldn't be the issue with the generator supplied power. But, the inverter probably doesn't isolate it.
Also, inverters that aren't wired quite to code (output neutral tied to shore neutral) pop shore-side ELCIs/GFCIs (for good reason). But, that is a different issue and wouldn't affect your generator or inverter.
I'm actually surprised your generator runs without generating enough output voltage -- most shut down in seconds if the AC output doesn't come up. This is true of my current circa 2015 generator and my last boat's circa 1977 generator.
So, I guess an interesting question is, if they don't five 110V, what do they give? And, how and where are you measuring the voltage?
