I just bought my third deep cycle marine battery in three years for my Rockwood Fifth Wheel. They keep going dead. I bring them indoors in winter and keep them connnected (plugged in) in the RV all ...
Charging while towing is usually more maintaining than charging, as the charge is pretty slow. I'm thinking your converter could be the issue, as it should do a good job charging, while camping/plugged in, and at home plugged in. Some converter/chargers do work better than others.
BTW...may want to take better care of wife, as that can get much more expensive than getting new batteries. :)