There are several videos on You Tube related to verifying the heating element in an electric/propane RV fridge. One link attached below. Also your fridge manual may have trouble shooting info.
If you don't want to do the Dealer warranty trip (understandable) and you are capable of safely working with and testing AC power circuits, then it might be worth a quick test to see if the element has failed open....... or something else is not working:
is 115vac even getting to the AC receptacle mounted inside the fridge exterior access panel; is the fridge control board (set on automatic) switching to AC power (from propane) automatically when working AC shore is connected; etc.? Note though I am not sure if this would void the Dealer/Manufacturer warranty related to the fridge.