FWIW, we also sometimes leave the dog in the motorhome with the generator powering the roof air when shopping, eating, or rockhouding out in desert heat.
However we have discovered one trick for ultimate safety from internal fumes when doing this, just in case: We close up the entire RV except for one roof vent with a multi-speed, reversible fan in it. We set the fan speed on LOW, and set it's air direction to AIR IN. This creates and maintains a small, positive air pressure inside the RV so no fumes can enter anywhere. The very small amount of air entering the powered roof vent to maintain the pressure is from way up high, where there won't be any generator fumes in the outside air.
P.S. #1 We also use this trick to keep dust out of the RV when traveling on dusty roads.
P.S. #2 We also have used this trick when touring the Southern U.S. in August so that we could leave the coach air conditioner running off the generator in order to sleep in EXTREME heat and humidity when drycamping. Having the generator run all night while sleeping also meant that we had enough "generator white noise" so that we didn't have to try and sleep with that incessant and loud-right-through-the-RV's-walls cicada sound drumming in our ears all night!