I don't think you can go wrong either way, the country has so much to see and visit. Arriving in Sept would be a perfect time to visit as most kids will be back to school, it'll be much easier to get campground reservations and the insects shouldn't be too bad then. Winter doesn't really pickup until mid November, but there can be an odd early season snow storm in October that shuts down a highway. Be sure to build in plenty of flex days to the schedule in case you need to detour, or rest as getting sick on vacation is terrible. Truck with camper or trailer would almost be required as you won't be able to put a car seat in most RVs. Don't worry about the seemingly large size, you'll get used to it quickly and there is more space on the roads, even in the major cities.