X2 on checking the 120VAC line voltage inside the trailer. You are describing what happens with low AC voltage.
If this is at a home shore power connection your 120VAC from the house may be too low to use.
In both my trailers connected to my garage 120VAC 15A and 20A receptacles I have one of these RV 120VAC VOLTMETERs plugged into a receptacle in the trailer close to the Air Conditioner controls. I always just glance over at the plugged-in 120VAC Voltmeter before turning the unit on. This voltmeter has the safe zone printed in GREEN.
just my thoughts
Roy Ken