Here is a valuable link regarding double towing. From the different things I've seen online, this one gives the most detail, including the last column which regards reciprocity for each state.
Keep in mind, that the legislatures of the various states can change their laws at any time. Thus, it would still be advisable to verify each state that you plan on towing through. The last thing you want is for some policeman to inform you that you will have to drop the second trailer until you get the RV out of state and then return for the second unit.
http://www.towingworld.com/articles/TowingLaws.htm
Terry