So long as you have sufficient gas in the tank, the generator is not likely to quit unless something goes wrong with it: oil loss, overheating, that sort of thing. If it's in good repair, it should be quite reliable.
Fumes can be a concern, but a little common sense goes a long way towards preventing trouble. Keeping the windows near the generator shut, not parking in an enclosed area where the fumes are going to collect instead of dissipate, making sure that the generator exhaust system is in good repair, and that sort of thing are important. While not really applicable for a rental, constructing or buying a gen-turi sort of arrangement to route the fumes above the roof is also a great thing to do.
Depending on the weather and how long you're at the attraction, you might not need to run the air conditioner to keep the inside at a reasonable temperature. Parking in the shade and opening some windows and vents, along with having water available for the pets, may well be perfectly sufficient.
