I have owned three absorbtion refrigerators. None of them would keep ice cream well in hot weather.
I have spent a lot of time in AZ and TX. I gave up on buying ice-cream any time it was over 80-90F outside.
My solution was to replace them with 10.8cu.ft. residential refrigerators. No problem keeping ice-cream solid and ice "dry" if you know what I mean.
My 5'er has two golf cart batteries, a 1000 watt PSW inverter, 300 watts of solar and a 25 amp shore charger.
This setup has served me pretty well for almost four years and 6000 miles. The batteries have lost some capacity over time and will probably be replaced next year. This season I have had to run the generator a bit more than past seasons.
We are working on our "new to us" rig that will sport 1800 watts of solar and a much larger battery bank (24 volt 430 a/h). No more generator needed! Well.. Not unless it gets cloudy :)
We love the space of the 10.8 fridges. They seem enormous inside compared to the absorption fridges they replaced.