You could safely do what you're suggesting with a panel and outlet, though it may not technically be up to code for a permanent installation. I wouldn't worry about that aspect of the code too much so long as the campground doesn't object. Do make sure you use suitable wire for the connecting cables; something like the cable for the RV power cord itself would be much preferred to Romex (which is definitely not suitable for outdoor use) or direct burial cable (which is only a little more suitable).
However, I would think about whether it's necessary to have so much wiring. Your RV typically should have an exterior outlet on it already, which I would think could be used for the deck/screen room power needs. If you're mostly concerned with lighting in the shed (as opposed to using power tools or whatever there regularly), a battery powered or solar powered light would not need any additional wiring. Something like
this from everybody's favorite supplier of cheap tools cheap, for example, may be suitable.
