I work in an industry that have used solar in some commercial applications, and I have one on my camper.
The solar controller I have has a way you can connect it to a laptop, and actually see what is going on, and look at the charging history, etc.
My ~200W system is entirely roof mounted. The idea of having your panels so you can move them around in your site, if trees are present, is a good idea, as long as you have a way to store the panels during transit so they don't get damaged. The benefit of having them on the roof is you don't worry about them when you're packing up or moving. My system will provide around 15A continuous charge in the middle of the day into a 12V battery bank.
Power is measured in watts. Your 20A circuit on a 120VAC plug is capable of delivering 2400W. Your controller can use up to 500W. a 500W solar system will provide this power under absolute ideas conditions, which means it's noon, and your panel is pointed at the sun, not just on flat on the top of your rig, during the time that the sun is fully out, during the day.
My camper has the fridge divider heater disconnected, which by itself used 10 to 12W continuous. We know that our solar system under trees can typically deliver enough juice to keep us going forever with lights, a fridge, and a Maxxaire adjustable roof fan running at 30% or slower all night. All of these devices add up to a power budget of around 10 to 15W continuous, or about three quarters of an amp at 12V, according to the controller (it measures what is being drawn out of the system, as well).
When you start thinking about running a microwave, air conditioner, or any other full size appliance, the game changes very significantly. There is a reason houses that are off grid have their entire roof covered in panels.
The solar panels are just the charging element of the power system. If we think about using something like an air conditioner, microwave, or anything that draws 1500W of power (I have no AC experience, but a quick internet search shows that even a small one would draw at least 1500W of power) If you just look at the batteries, the Trojan T125s that I have two of to give me 12V have reserve capacities that diminish as power draw goes up. Their specs are 132 minutes of reserve at 75A, so if you draw 900W of power out of the system, you will go from fully charged batteries to dead batteries in a bit over 2 hours. The characteristics of these batteries is the slower you pull current out of them, the better they are at lasting, so a 450W draw means you can at least double reserve capacity. You can run additional sets of batteries to get additional capacity, and to improve how much of the charge you are generating gets used. Batteries have charge rates, and you can run into the situation where your solar system can't "dump" the power into the batteries quickly enough due to battery capacity. If I were to set up a system for AirCon, I'd look at a minimum of 4 of the T145s, if you have room. This would allow you to run the 1500W air conditioner for about 145 minutes, leaving some room for the conversion efficiency of your inverter. (Keep in mind that the conversion from 12VDC to 120VAC comes at a power conversion "cost"). The next problem is the initial startup draw of the air conditioner. The one example I found on the internet draws 4200W on startup.
So, if you have 500W of solar, that can charge your system for half the day, you kind of have 500W for 12 Hours "banked".
So, in essence, if you have a small AC unit that draws 1500W, and it is running continuously, you would have enough jam to run it for 4 hours, assuming no "startup" penalty. The efficiency of both your solar controller, and your inverter will play into this, and the more batteries you have, the better things will be.
Hope this helps. If anyone else finds errors in my math, my apologies. But I checked a few times, and this seems reasonable. I hope this helps you out.