sounds like to me it might be shorted cells in the battery bank... But you say when on shore power both AC side and DC side (with batteries connected) works ok. Only happens when you start up the generator which switches the shore power transfer switch and selects generator to run the AC Distribution Panel.
Something not adding up here. The shore power and the generator feeds the same point depending on which position the transfer switch is in...
Keep in mind both the converter/charger DC output and the 12VDC coming from the batteries both feed the same point on the 12V Distribution Center... The 12VDC circuit breaker is only on the battery side...
Sounds like a big load is causing the the generator to trip out...
The only MAIN 12VDC Circuit Breaker I can think of is in-line between the battery and the 12V Distribution Panel mounted close to the battery terminals. Its purpose is to protect the wiring in case a cable short to frame ground.
This is a very simplified block diagram of the 30A AC and DC Power Distribution in a regular trailer setup... Might give you a clue...
Roy Ken