I run it on battery when towing, and have a switch to shut it off when I stop (to eat, or whatever) so the battery doesn't drain while the TV isn't running. If the only time it's running is when my engine is on, then there's no issue with battery charge, and I always get to the campsite with a full TM battery and a cold fridge
Yes, I pre-cool for 24+ hours before a trip, too. Then we load it up, switch to DC/battery power, close up and go.
(Note: The Elkmont has a different fridge than the fold-down TrailManors, so Brulaz' statement may or may not apply to you.)