The dash air is plenty powerful enough to keep the RV cool in nearly any conditions; it's generally equivalent to two or so roof air conditioners in capacity. The problems are getting sufficient and properly directed airflow through it to use the capacity and get the cooling where you want it. One thing that seems to help with my RV is to open the rearmost roof vent (with a vent cover, of course) a little while underway in order to promote cool air moving all the way through the RV--or, in cold weather, heated air.
It certainly is possible and sometimes reasonable to run the generator and roof air conditioner while underway, too. Occasionally on very bumpy roads some generators might stumble a bit, but generally it's no problem at all.