Recharging with a Generator

The charger is already set to run off the generator. If you want to charge the house batteries faster you will need a portable battery charger. Use an extension cord to run from the generator to the charger and then connect the charger to the battery or batteries, as the case may be. Just remember, that too high a charge rate will cause internal problems with the batteries and will kill them faster than a slow steady trickle charge. Personally I would not do this except in case of an emergency. The generator & charger are designed to give you the best performance and extend the life of your batteries.

We just plug the shore power cord into the generator. That way the RV has shore power, and the converter can handle recharging the batteries.

I leave the water heater on gas to free up some amps for charging rather than heating the water.

You may want to upgrade to a three stage converter/charger. My Magnetek 6300q is obsolete so I'm going with the 45 amp converter kit.
You may still need to run your generator for many hours on some days to fully charge. I understand that I will be able to go from about 50% state of charge to 80 % soc in a few hours. I understand that I will be able to do this for a number of days and will then have to run possibly 10 or so hours to fully charge and avoid sulfation/stratification. There are many posts on here from the battery gurus about deep cycle charging.

http://www.bestconverter.com/MagnetekParallax-63007300-Upgrade-Kit_c_64.html

I would stick with plugging the trailer into the generator even though it takes a long time. It may have a good quality charger built in. Basically a good external automatic charger will do the same thing. I'm not sure how the Honda charges the battery.