Assuming you are running the generator for an hour or two anyway to cover high demand loads...just plug into the generator and call it good.
The trailer doesn't know if it's connected to a pedestal or the generator.
The "converter" which is really just a battery charger (never understood why the RV industry made up a new term) will take the 120v AC power and use it to charge the 12v DC batteries.
Now if you continue to do a lot of boondocking and get into solar and large battery banks, you may want to consider a better converter and battery monitor system but keep it simple at first. If you do make the jump to an extensive 12v DC system, start doing an energy audit of what you use and for how long. This will allow you to determine you needs in terms of solar and battery bank size much more accurately.
