I have had the above problem for a while. I totally agree with Eric . I am using the Pepwave surf 200. I turn off the wifi on the computer. Then go to IP for the surf and sign in to the hotel wifi. This brings up the portal on your computer. You then move the ethernet cable to the remoterig after maneuvering through the portal and the remoterig works. The surf 200 acts as a wifi client and since it has NAT, devices behind it will automatically connect the hotel wifi. Hope this will add some helpful info to Eric's explanation (which is excellent). It's simple but those of us who are not IT techs can miss it easily. Ports in the hotel can block the remote rig also but I am using 5065 and have no problem. Good luck.
73, Jerry W4YB