A couple of weeks ago I visited the Peterson Automotive Museum in Los Angeles. They had on display a variety of camping vehicles dating back to the early 1900's.
It appears the first motor touring vehicles were handmade out of necessity from existing vehicles, like the Model T and such. As the early pioneers travelled west, they tweaked their cars to fit their specific needs. Back then these vehicles were pretty unreliable and the country's roads were barely developed, so it made travel very treacherous. So, you 'could' say it was Henry Ford and his consumers, but let's not stop there....
Companies such as Airstream (debuting in 1934) created the "travel trailer" which was less expensive to maintain because of the lack of engine, etc. Before the traditional RV as we know it today (with an engine) existed these travel trailers were most popular. Remember, in these days it was pretty rare that someone could actually afford two vehicles in their household. They were considered fortunate if they had a black and white TV. So the trailer was king and Tin Lizzy (personalized Model T) campgrounds sprung up all over the place.
When World War II started nearly all production halted completely. It wasn't until well after World War II was over that the RV industry really took off. Many small companies began developing motor homes in the U.S. and popularity was growing in Europe as well. But it wasn't until 1966 when the first Winnebago rolled off the assembly line that RVing really took off. Winnebago used an assembly line which allowed them to sell their vehicles at nearly half the cost of its competitors at the time. But the answer is not Winnebago, read on ...
Well before Winnebago there was Bertram Hutchings, Founder of the Winchester Caravan company who experimented with his 'motor caravan' in the 1930's. It didn't take off, but it did spur other ideas. Other historical manufacturers include Cayo RV Corporation of Benton Harbor, Michigan; Veseley Corporation famous for Apache plastic-sided pop-ups, and for a little while General Motors. In Europe the caravan manufacturers were Hobby, Swift Group, Explorer Group, Bailey, and Hymer.
You might have been looking for a single manufacturer, but I'm not sure if anyone has the answer. All of these RVs were developed across the nation (and world) during a short period and no single national company existed at the time. Since communication and trade (across state borders) were also still in their infancy, no one really knew what the others were doing.
Well, I hope that helps! This history has been a long time interest of mine as you can tell.
Back to the museum.... Most of the items at the museum focused on the trailer aspect rather than the "RV", but you can find more information at the website below.
Peterson Automotive Museum
RV Hall of Fame
Wikipedia & my head