Interesting scenario. I'm doing much the same as you at home currently. If I recall correctly my Airport Extreme has to connect to the source internet by ethernet cable, it can't receive internet by WiFi. The Airport Extreme is a router but not an access point.
What I do when traveling is enable Personal Hotspot on my iPhone then access that signal on my MacBook Pro. My phone carrier is Verizon and most of the time it's better than RV park WiFi. You might check into the MiFi product from Verizon for data service. At work we using the MiFi product and can support several connections to it on the Verizon cellular data network.
Good luck finding a solution.