Solar system hookup
Ok, lets make sure we are using the same terms. An INVERTER takes 12 volts DC and provides 120 volts AC. A CONVERTER takes 120 volts AC and provides 12 volts DC. It often also includes a so-so battery charger.
So no, your INVERTER should have no interface with the 110 volt outlet at all (unless the outlet is otherwise not connected to any source of power, and you are willing to live with it being the only outlet supplied by the inverter, a seemingly ineffective setup.
Many 5th wheels don't have a generator, so let's assume you have only the 'shore power' cord and the inverter outlet as your only sources of AC power. Sounds like the current setup is to plug the trailer 'shore power' cord into the inverter to provide power when a hookup is not available. Inconveniant, but should work fine, keeping in mind that the 15 amp socket should never have a draw greater than 15 amps/1800 watts (except for transiants) while the trailer 'expects' to have 50 amps available. Further more, 50 amp trailers actually have 2 circuits, and that adapter probably feeds only 1 of them, leaving 'half' the trailer unpowered.
What is the rating of the inverter (maximum amps/watts and sustained amps/watts)?
The best way to wire an inverter into the coach is to have it very close to the battery bank, connected with very large guage wires. Then run 2 appropriate 120 volt line (or a 240 volt line) to the junction with the shore power cord and into a 'transfer switch'. This can be automatic (switch to shore power when available otherwise power from inverter) or manual (select your power source).
All components should be rated at the maximum current to be used. For instance if you have a 6000 watt inverter, all components should be rated at 50 amps. If your inverter is much smaller, you can use lesser components. Or you can still go with 50 amps which would allow you to upgrade your inverter some day.
