The easiest way to damage an electrical appliance is to run it on insufficent voltage/amperage, to run all the appliances in the trailer you need to supply the required minimum voltage of 115VAC at the required amperage. The trailer plug utilizes a 30 amp circuit on 115VAC to run all items in the trailer at the same time. If you use extension cords not rated at 30 amps or circuits that can't supply the required 30 amp you run the risk of damaging the appliances.
Some time ago I was camping up my Niagra falls and quite a few people where having troubles with their A/c units, one fellow had a plug in voltage meter on his unit and it was reading 92VAC instead of the required 115VAC. Seems like the park was unable to supply sufficient amperage to handle the demand and the voltage was dropping
I use an RV voltage meter to monitor type voltage these are relatively cheap and could save you hundreds in expensive appliance repair
AC Voltage Meter - Intersource Enterprises D10-170 - Voltage Monitors - Camping World