JacksonJack,
We have traveled for years towing and have started the generator to cool the RV 30 minutes or so prior to stopping for lunch, siteseeing, or etc.... We have never had a problem doing this & our furry camping companions appreciated it. In fact when traveling in our motorhome, we would run the on board generator and cool with the roof AC instead of using the dash AC because it did a fantastic job cooling.
Happy Camping and enjoy, enjoy, enjoy the West.