Here is pictorial diagram that might help understand how the single valve works.

This pictorial claims to be on the Winnebago trailers showing check valves installed.

I personally like the three valve setup much better as you more control of what is going on I think..

Certainly sounds like you are mixing hot with cold water with your one valve when you are getting warm water out of both spigots... That happens on the three valve system when you have the center valve opened up along with the other two valves.
Good luck tracking down your problem - doesn't sound like it will be all that difficult once you start really looking at things real close.
Roy ken