Somewhere in between depending on what end result you want.
twinboat's plug in the appliance when you need it, is the simplest approach, but may not work for your fridge and anything where the plug won't reach the inverter outlet(s).
The other option which is a bit more complex, would be to feed the inverter output to the same circuit that feeds your shore power and generator 120VAC output to the wall outlets throughout the coach. An auto transfer switch would be required to prevent everything from trying to share that circuitry at the same time. There will already be one auto-transfer switch to separate the shore power 120VAC from the generator 120VAC going to your coach outlets (unless your shore power cable is a "manual" plug into the generator output, like my Navion).
So, it's a little more complex, but it can be done. I would think an electrician that knows/understands RV wiring and power systems would be able to help you with the second option. Some RV repair shops might have such a person available. Any shop that does these kinds of 12VDC/120VAC/converter/inverter/solar/battery conversions and/or upgrades may also be able to advise you on it. Half the battle is finding the right shop, if you go that route.
2018 (2017 Sprinter Cab Chassis) Navion24V + 2016 Wrangler JKU (sold @ ????) - 2016 Sunstar 26HE (sold @ 4600 miles) - 2002 Roadtrek C190P (sold @ 315,000kms)