residential refridgerator

Make sure the inverter is large enough to handle the inrush current of the fridge compressor at start up. I tried a 600w inverter, initially. It would not handle the large inrush current. I now use a Xantrex Prowatt 1000w and it is silent and handles the load easily.

If you want automatic transfer for the inverter and the fridge only, there are single circuit transfer switches available.That is an easy installation. If you want whole house transfer for powering other circuits, you'll need a transfer switch capable of that whole house load, typically 30 amps with a travel trailer.

You'll get more specific advice by listing your RV, the model of fridge you are going to use, and the components of your 12V system.

Residential refers do NOT need 12VDC. They need 120VAC.
Most installers simply have a dedicated circuit for the refer to run off of. Batteries, inverter, refer. No need for a transfer switch. But if you insist on one, then you would add it between the inverter and the refer.

Yes, the residential fridge itself doesn't need 12VDC, but the inverter to run it on 120VAC when not on shorepower sure does. Making sure the 12VDC system is up to the task is essential.

I had a standby type Xantrex Sw inverter that automatically transferred to 12vdc input when the ac input is lost. It would have been what you were looking for except it only had 600 watt output.

Xantrex does have a 1000 watt model but I don't believe it has its own automatic transfer switch. You could use it but would probably have to incorporate an automatic transfer switch.