An "out of the box" solution to an RV inverter is a computer Uninteruptable Power Supply (UPS). I mention this because you can frequently find ones capable of about 1000W, cheap, on Craig's list because their internal batteries are dead. Remove them and hook up external batteries. They are nice because they can be plugged in between your shore power/generator and the entire trailer AC load and they kick in automatically.
The small, low cost ones are modified sine wave. But if you check the spec sheet carefully, you will see that the medium and large sized, better "quality" ones are true sine wave output.
There are 2 down sides.
- These usually require a 24v supply. This is actually a plus because 2 deep discharge 12V batteries will give you more run time than just 1 ! They do have built in 24v battery chargers.
- Second, these things really are not designed to be run under full load continuously. Additional fans will likely be required.