You should have combination charger/converter/inverter check it for three pins or whatever the proper nomenclature is and make sure they are all pushed in. Is it dying I don't know without looking at it Find a good RV Repairman.Check your house batteries. The lights etc run on or though them. Some units may not have a refrigerator that runs on ac. But first find the house breakers. Our has two one each for the heat pumps and two more one each for the two 120 volt plug ins circuits which includes the convection/microwave
However it does sounds like the inverter but unless a surge got to it it may still be good. If you replace it get the next higher rated unit.
The Inverter should be in the compartment next to the battery compartment which should be dry and watertight.