Hi NeverFirst, I think you are doing this the other way around. It would work the way you describe but it may be better if you use the Mac of Edimax.
1. Power on Edimax
2. Connect to Edimax from your laptop/device
3. In Edimax wisp mode select the hotel wifi you want to connect to
4. At this stage the Edimax will reboot
5. Make sure your devices are connected to the Edimax SSID
6. From any device browse the net - you'll be presented with a portal login
Note that the internet provider is now seeing the Mac of the Edimax not your device behind it. Authenticate and connect. The Mac of the Edimax will now be associated with the connection.
Even if you power off/on you will retain this setting subject to duration of connection governed by the internet provider. I can't answer why Edimax is not retaining Mac cloning settings because I've never used it this way.