In most cases an inverter is not especially helpful. I have a small one which I have never used but which I keep in case I want to run the TV or the cake beater while in the middle of nowhere.
Here are the basics. I apologize if this is familiar material but I sense that you may be new to this.
Almost everything in the traylah will run on 12 volt
battery power. The only things that won't are the microwave, air conditioner, the (usually, it depends) TV, and the outlets.
The most common situation for most people while camping is to use shore power, which means to plug in the trailer cord into an outlet. Any park that allows camping, and the corps of engineers campsites, resorts with RV sites, and commercial campgrounds, all provide this, sometimes for a few dollars extra a night. If u are staying at a friend's place or in your own driveway you can plug into a regular outlet with an adapter instead.
When you're plugged into shore power, the converter charges the batteries and runs the 12V
lights and appliances. Also, the outlets in the trailer are powered from the cord, as is the microwave, air conditioner, and TV.
If ur not plugged in you can run usually for a night or two on the trailer battery, more if u have several batteries and conserve, less if u run the furnace a lot.
When u plug into ur generator using the adapter 2air recommends, it's like ur on shore power, the battery charges, and everything runs on the generator. If u have both generators going at once you can run the air conditioner or the microwave, maybe even both at once.
In general it is not practical to run the air conditioner or the microwave off the inverter because the battery capacity isn't sufficient to run them for very long. So, inverters are mostly useful for electronics and gadgety stuff (like the beater I use to bake a cake, or the cordless drill charger) that doesn't require much power.
Heating appliances are best replaced by the stovetop equivalents or used on shore power only. There are stovetop toasters, for example.
You can obtain 12 volt
versions of many small items. I have a 12 volt charger for my phone and my computer. There are 12 volt fans, and 12 volt chargers for cordless tools, 12 volt electric blankets, and 12 volt TVs. In most cases these products work better are are lighter, cheaper, and less fiddly than an inverter.
I know it's a lot of stuff.
Keep asking questions.
Spend a night or 2 camping in the driveway.