Not knowing what type of connector is mounted on your RV and how it is wired, makes diagnosis very difficult. if you have a four wire connector on the towed and the RV, there isn't much the towed can do to drain your RV battery.
My Bounder had a 125amp alternator and that will run a lot of stuff if yours is close to that. I'd check to se if there is something causing the charge control of the RV to open when you're towing. Maybe it's time for a trusted mechanic to check your alternator and charge control circuits.
