All of the items you are having trouble with are 12 vdc. Note: the reefer has to have 12vdc for the controls even when 110v is selected. You may well have a neutral issue that needs to be corrected but my best guess is that your converter malfunctioned and reset when you disconnected to tow to the campground. Why did the converter malfunction??? Again, best guess, low voltage when A/C was attempting to run.
Disclaimer: I ain't no stinkin' electrician.
'02 Ultimate Advantage 40J Spartan MM - Cummins ISC
2013 Jeep Rubicon JK Unlimited