With a 21 year old RV you need to have everything checked and or serviced before leaving on a trip, especially in the desert.
You stated that you "plugged in power and turned on gen and ac". Why would you do that? If you are plugged into power don't run the generator too. If the A/C doesn't run on shore power you have A/C problems too.
Other possible generator shutdown issues are a bad temperature sensor. Engine will start and run for a few minutes then shutdown. Check the code the generator give you after the shutdown.