Hopefully, your refrigerator will have an "auto" setting. If you use that setting, when you are not plugged into electric, it will automatically switch to LP until you plug in again. That is if you turn the gas tank on. I think most will have this feature.
We use our generator to make a pot of coffee if we park at a Walmart for the night, to warm up lunch at a rest stop, or if parked and the power goes out in a storm or something. We are usually already parked for the summer before it gets so hot we need the A/C when driving. There is dash air that can keep you comfortable in mild warm weather. We do plan most meals on the road for things that can be cooked on the cooktop, or a hot roast chicken from Walmart, or takeout.