From what you've described, I feel you may have an inverter that is using your battery to power your TV. If so, turn it off; you should have a switch to do this while traveling or storing your camper.
Next, while towing, you should only have your two-way fridge operating on propane and 12-VDC for the control board and your camper's interior lights.
If nothing else is turned on while towing, your battery should easily have enough power for a day-long trip.
If this isn't so, how old is your battery? Does it have water in it? Maybe it's time for a new battery if it can't hold a charge.