Every state has different traffic laws. To be completely accurate, you'd have to check the passenger restraint laws in any state you plan to travel through. But remember that just because it's legal doesn't always make it right.
In general terms... although not recommended from a safety perspective (see the thread
Moving around in a moving vehicle - NO WAY!), there are often no laws in particular regarding RV passenger restraint BEHIND the cab area. That is because RV's fall into a gray area of the vehicle code... they do not fit into the category of passenger cars (too big and heavy) and are also not commercial trucks (privately owned and not operated for profit).
As a motorhome owner, I always had all occupants buckled while the RV was moving. I'm generally somewhat of a safety freak and discouraged movement under way, but I'll admit we did make occasional exceptions for a quick bathroom trip or snack run from the pantry. This always depended on the point in our trip (whether there was a place to stop), type of road we were on, current traffic conditions, etc.