Not sure how you connected up your generator but what we do is connect the 30A Shore Power Cable directly to the generator using one of these RV30A-15A "DUAL" HONDA adapters from Amazon that plugs into both sides of the Honda 120VAC receptacle. The 30A shore power cable will plug directly into this adapter...
You cannot use the little adapter cable that comes with the 2KW Honda generator that plugs into the BAT CHARGE connector and get any good results. - Have to plug the trailer shore power cable into the generator 120VAC receptacle to charge your battery..
Doing this will power up your whole trailer so you may have to flip a couple of 120VAC breakers to turn off some heavy current items. What the game plan here is to allow your on-board smart mode converter/charger unit to re-charge your battery back to its 90% charge state in as little as 2-3 hours of generator run time. You can tell if the battery is at 90% by measuring at the battey terminals for 12.5 VDC using a mulitmeter after you have stopped charger for a few minute after the battery settles down. You should watch your battery drain when you are running off the battery at camping off the power grid sites and when the battery voltage drops to 11.9 to 12.0VDC (50% charge state) this is the time you should start re-charging your battery by plugging the shore power cable directly into the 2KW Honda Generator using the special DUAL HONDA adapter. If you are at a generator restricted run time location you will have to wait until 8Am the next morning to run your generator probably.
This is what we do with our off-road POPUP every morning at 8AM when camping off the power grid. We usually are allowed to run our generator from 8AM-10AM and then again from 4:30PM-7:30PM on most of the East part of the US that has generator use restrictions.
Plan your battery drain to not get the DC Voltage below 12.0-11.9VDC for the day/night battery run, recharge the battery the next day back to its 90% charge state and then you can do this all over again for that days/night battery run.
Doing this every day extends our battery bank to be used for the entire camping camping trip. This only works if you have the smart-mode converter/charger unit installed on your new RV. Post the model number OF THE CONVERTER/CHARGER UNIT and folks here can tell you if it a smart mode converter/charger unit.
We love camping off the power grid...