Wiring an inverter to run the whole trailer is alot more simple than some seem to make it out to be.... Pick up a transfer switch (Go Power makes an easy to wire unit).
Disconnect the main 30A power and converter charger from the control center.
Run a new wire (14/2 household wire from the converter to the transfer switch.
Connect the new converter wire and shore power wire to the shore power input side of the transfer switch.
(leaving the converter wired as it came with the trailer will cause the inverter to attempt to charge your batteries from your batteries.....)
Now run a new section of 30A power cord from the transfer switch house side back to the converter.
Install the Inverter of choice as close as physically possible to the batteries and use the proper guage wire direct from the batteries to the inverter... BTW wire is not cheap but this is the most critical part of the install.. Doing this wrong or using under sized wire will very likely cause a melt down and worse yet a fire.
Also install an appropriately sized breaker at the battery.
Once the inverter is mounted run your 110v wiring (again appropriately sized), from the inverter to the Generator side of the transfer switch.
Now that the wiring is complete remember to turn the fridge to propane only when running the inverter or you will kill your batteries very quickly with the fridge defaulting to shore power.
If you plan to use the microwave (which kills batteries quickly) you should use a pure sine inverter, minimum that may run it is around 1000w if nothing else is running, I use a 1500w.
Modified sine will run the microwave but only at about half it's efficiency.
Good luck with the install and have fun learning just how quickly you can drain batteries.
While pure sine wave is the better way to go it is more costly. A good quality modified sine wave inverter will run most things with no issues.
I should probably mention this... If you have no knowledge of electricity pay a professional to do it properly...