I have done this successfully with my RV.
This needs to be absolutely fool-proof so you do not back-feed the inverter with shore-line power I think the shore-line power will not care about the inverter feeding it.
Do not bother messing with the breaker box.
Since you just want outlets powered by the inverter then this is easy.
Buy an A-B switch, a toggle switch that can switch between two different lines.  You will use this on the hot side.  Feed the hot wire, usually black, from the breaker box to your new switch.  Connect to one side, doesn't matter which.  Feed the hot wire from the inverter to the switch on the other side.  The two sides will be input, from shore-line or inverter, and the center will be output, to outlets.
This way you are unable to have both sources feeding the outlets, and the inverter cannot feed the breaker box either.
Use an electrical box- junction box for the switch.  Mount it anywhere you like.
Likely the inverter does not have any output other than the plug.  Just use a 3-prong plug to plug into the inverter and you will make bare wires on the other side. *
The white wire, or neutral wire from the inverter will simply connect to the shoreline breaker box neutral wire white wire.
The green ground wire will connect to ground, and this can be done at the breaker box or directly to the trailer frame, or battery negative.  I would go to the breaker box unless the neutral is grounded.
If you want some appliance to run off either inverter or shoreline then you will need to wire that into the outlet side, keeping in mind that you might be taking it off its own breaker switch to do so. - assuming said appliance is hard wired into the breaker and not plugged into the outlet.
The things you want to run off shore power and not ever inverter power will need to be wired into the wiring before the A-B switch so they have only the ability to run off shoreline power. You probably don't need to worry about this.
The quick and dirty way to power outlets from an inverter is to use an extension cord with male plugs on both ends.  Plug one end into inverter outlet and the other end into any camper outlet.  This will power up the breaker box too and everything else, as well as the plug used to connect to shoreline. Electrical shock is possible if you touch the camper's male plug end.  AND you will destroy the inverter if you forget to disconnect this and plug into shoreline.  Like I said, quick and dirty.
* Another option is to use the Dirty method only, ONLY, to connect the ground and neutral wires.  Use the home-made cord with two male ends to connect one to the inverter and the other to any plug, preferable one out of the way or hidden in the dark spaces.  BUT, run the hot wire, black, as a bare wire and connect to the toggle A-B switch as described above.  BE VERY SURE THAT THE PLUG CAN NEVER COME OUT.
Sometimes camper electricians do not follow code, so double check that the white and black wires are neutral and hot.