I use my 2KW Honda Generator all the time to charge my 30A Trailer batteries but plugging the trailer 30A shore power cable directly into the generator 120VAC receptacle using a RV30A-15A "dogbone" long adapter. You can pick one of these adapters up from WALMART.

This will allow your on-board converter/charger unit to re-charge your trailer battery. If your on-board converter/charger unit is a smart mode technology then you can re-charge your trailer battery in a three hour generator run time.
If you do not have a smart mode converter/charger unit then its best to pick up a smart mode portable charger like the Black and Decker VEC1093DBD 40AMP portable charger and plug this into the 2KW Generator 120VAC receptacle and use the portable charger battery cables direct connected to your trailer battery.
The 8AMP connector on the 2kW Honda Generator is way to small of DC AMPS OUTPUT to re-charge your trailer battery. It would take days to complete the process...
Roy Ken