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There are a few different national RV companies. Cruise America and El Monte are two of the biggest, although they are not the only ones. For the smaller "caravan" type RVs, those are more rare, and the only national company I'm aware of that offers them is Escape Campervans, but other forum visitors have been happy with them.

Keep in mind, however, that one way rentals of any car or RV are going to mean extra one-way drop fees, and those fees can get quite expensive. That would be the big potential problem of doing a mix of flying and driving. With 5 weeks, you could go one way across the country and drive the whole thing, one way, pretty comfortably. If you do split it up, you might consider doing a pair of loops, where you start and end in one city in the east, fly west, and then start and end in that city again.

Also remember that RVs are not the only way to do a roadtrip, and they are not the cheapest way to do a trip. They are usually more expensive than cars/motels, and if you plan to spend a lot of time in cities, then they can be a challenge to operate and find camping. However, if you are spending a lot of time in National Parks and other natural areas, they can be a great lifestyle choice that can add to the enjoyment of your trip.