[wingnut60]

Your 2 6volt batteries are wired in series to product 12volt--use only the 12volt side of the charger.
Take this time to purchase a nice multi-stage charger--Schumacher makes many good ones--lots with digital readouts.
You have the connections right--just be sure you are recognizing the posts correctly. RVs have white wires as the negative, and red or black as the positive. You can use either the poles on one battery, or positive on one, negative on the other--it will charge either way--but probably better to use one pole off each battery.
As to recharging at the house--plugging in a household extension cord will use the converter to charge the batteries--no need for 30a or 50a. You would just need the adapters to get from your 50a trailer to 30a to 15a. Or you can go directly from 50a to 15a with the right adapter. The converter (battery charger) does not care whether it is 50a/30a/15a coming in, it will work on any of those as long as the adapters are correct.
Be sure when you get the 50a setup that the electrician understands this is not 240 volt 50a, it is 120volt.
Joe