It has already been stated that towing doubles in Wyoming is LEGAL (just as it is in Montana).
IIRC, the first trailer does not have to be a fifth wheel in Wyoming (it doesn't in Montana).
The second trailer MAY have to have brakes capable of being controlled by the driver. (it does in Montana, although a lot of second trailers don't)
AFAIK, California is the ONLY state that requires a CDL Class A with Doubles Endorsement to tow recreational doubles. Supposedly, so I have read, that is because that is the only license issued in CA that can have a Doubles Endorsement put on it!
YES, a good strong receiver hitch must be bolted or welded to the frame of the first trailer. YES, there must be provisions for lighting the second trailer.
Check the Wyoming laws regarding trailer brakes. It may be that the second trailer must have brakes, regardless of weight. It may also be that the brakes on the second trailer must be capable of being controlled by the driver independent of the first trailer's brakes. Also, check the maximum length of a truck/trailer/trailer combo in Wyoming. In Montana it is 75 feet, but I don't know about WY.
DO NOT trust ANY list of towing laws that you might find on the internet. EVERY one of them I have looked at is inaccurate! The actual laws are readily available at the WY GOV website. I have researched the MT laws regarding towing, but I have not looked at the WY laws, since I don't live there anymore.
Good luck in your research and in your towing.