You have the basic wiring plan correct but are missing the piece about the transfer switch. You should have either an inverter with it's own auto transfer switch or an independent transfer switch.
It might only take one instant, one time, to do some serious damage to the electrical devices in your rig if two power sources are online at one time. In your specific use, it may be easier to establish a subpanel with just the few circuits powered that you intend to use.
Transfer switch choices. In fact, I'd give the folks at Best Converter a call and ask them what they think.
RV electrical. There are many good ideas here about wiring and inverters.