"Devind33".....There is a cleaner way with less worry to achieve your goal. On your new inverter, you should have a 110 volt (IN) connection and a 110 volt (OUT) connection, since you said it had a transfer switch.
You'll need two lengths of Romex that are long enough to reach from your new inverter to the breaker panel on your trailer. If you can identify a breaker in your 110 volt breaker panel that powers the items (outlets) you want to use, you just disconnect the wiring (Romex) from the output side of the breaker, and wire nut one of the lengths of Romex to it. The other end of that Romex is connected to the 110 volt (IN) side of your new inverter. The other piece of Romex is connected to the 110 volt (OUT) side of the inverter and connected to the breaker where you removed the first Romex connection.
Basically, you're running that one breaker through your new inverter and then back to the outlets that it supplies. It's a pretty easy job as long as you can feed a couple leads of Romex up to your breaker panel. Run the Romex through some flexible electrical pvc under the coach between the two.
If you new inverter has two outputs, you could run two circuits form your circuit breaker to the new inverter, giving you even more inverter powered outlets.
No matter what you do, the inverter needs to be mounted as closely to the batteries as physically possible. The shorter the 12 volt cables the better.