Jerry's right. The converter will do a better job of charging than the DC output on the Honda. Just plug the trailer's power cord into the adapter cord that goes to the twist-lock connector on the generator, and start the generator up.
While it's charging, you can use the 120VAC things in the trailer.
The trailer has a converter in it that charges the batteries, as well as supplies the 12 volts for the lights, fans, etc in the trailer when you are plugged into 120VAC electrical powre (so that isn't coming out of the batteries).