You really need to do some research to get an understanding of what device does what, what is needed & understand power management.
The root of it all for drycamping is having an adequate battery bank.
Next is conserving that battery power. Turn the water heater OFF. Turn the 120VAC supply to the fridge OFF.
Connect the inverter to the battery bank &, since you are only talking about using wall outlet circuit, the output to the circuit breaker/s feeding those outlets.
VERY IMPORTANT: Before connecting to shore power disconnect inverter output from trailer 120VAC simply by pulling plug on the front of the inverter. Failure to do so will result in expensive backfeeding, an explosion, smoke & the destruction of the inverter. Don't worry about how I know this.
Even now, with a pure sinewave inverter/charger I operate my inverter manually rather than leave it to its automatic feature to make the switch.