Yes, with your model that would be an issue. Access to the fridge when closed up was one of the deciding factors when we were pup shopping. Even without the switching issue, I like being able to load up the fridge without having to open the pup. Or even to check the fridge when we make stops. Since you are hooked up to shore power to cool the fridge down, why not switch to DC as you close up and leave the shore power hooked up until just before you pull out. The fridge should stay on through the converter. Then when you hook up to tow, disconnect the shore power and the fridge will then stay on battery for the tow.
HTT: "EscapeII" 2016 Shamrock 23WS (current)
PUP: "Escape" 2010 Rockwood HW 277 (gone)
TV: "Bruce" 2011 Dodge Durango V8 Hemi Crew
Just us gals (me, Sis and our daughters)
Traveled 19520 miles and 209 nights in 7 years and counting