It might possible to design something where you connect the core to the hotels network. Then you have the core present the same pages to your smartphone which it sees. Then when you click it relays those clicks back to the hotel.
In the same vein as this topic :
Although it would be quite a bit of work, probably only worthwhile for an actual product.
If the hotel uses mac addresses and you could try spoofing the mac of the core with your router, accepting it and then it may start accepting the core once you change the router mac address back to its original.