Out of the factory you are probably woefully under powered in battery bank capacity. Do you have space to increase it? My last 5er, an Alpenlite 34RLR Ltd., had 6 6V batterys & a 2000W inverter charger. One heckuva setup for an out of the factory 5er.
You need to fully understand what you have & what you need to have to power it all. Lots of good advice, including turning the fridge off at night & not opening the door. During a nice cool night it will not lose much chill at all. I used to do this onboard my boat which had 2 small 12V fridges.
For increasing battery bank capacity consider changing the type of battery used. Wet cells need ventilation. AGMs can be put anywhere. They can be put inside somewhere. Put them in the basement area. Put them in the living area as is commonly done in the marine applications.
In the meantime make sure that your inverter is not powering anything else major