Regarding running the air conditioner and the microwave at the same time; on occasion, we have also encountered this in campgrounds. I suspect that campground circuit breakers are often old and/or weak due to being out in the weather all year, and they may trip at less than 30 amps. This guess is based on the receptacles that are often worn, discolored and sometimes chipped/broken. If you use the 20 amp circuit, the combination of air conditioner and microwave probably exceeds 20 amps.
We now consciously do NOT use both appliances at the same time, even when on our own generators. Also, don't forget other high-current devices that others in your family may be using in the other room; e.g., a hair dryer.