You should be able to charge both batteries - the charger should go on "current limit" if they are near discharged. When you tow they should be charged from the tow vehicle.
I always have 2 batteries in the RV. I purchased a battery box designed for 2 6V batteries to contain them. Modified it to use the vent rig from the original battery. No problems charging the batteries.
Only need 2 batteries when I dry camp - twice a year at Watkins Glen race track.
Before I install the batteries in the spring I pre-charge them with a battery charger.
I have a 30 amp RV plug mounted in the outside of our garage and leave the RV plugged in - close the breaker feeding the RV plug to charge the batteries once a week when not using the RV.
