battery charging

I would agree the honda can do the job but only if the charger is not trying to put 10-15 amps ac charge in. Not the same Charger but my inverter/ charger can be set to only use 2-3- 5 etc amps ac thats devoted to charging. Is it a ground fault or is the Generator going into "overload" and cutting itself off? The motor runs normally but wont generate. Thats what happens to mine is if you overload it. you really don't know its happened other than the inverter is still inverting, and the Gen overload light flashing, is that the light?. If your batteries are low then the charger will throw everything it can at the Charge which may be the entire 15 amps the generator can produce, leaving nothing for the refrigerator etc.
If it is a true Ground fault I haven't seen that. My small generator 2000w works fine.