When you're connected to the hotel wifi, can you navigate past the "can't connect to the internet' dialog? If so, you might be able to sign in to the hotel wifi using the ouya browser under MAKE -> sofware

Also, for recovery mode, I suggest using ADB and telling it to reboot into recovery. http://www.howtogeek.com/125769/ has a good guide on setting that up. Then you have to add the OUYA manufacturer ID so it shows up, https://devs.ouya.tv/developers/docs/setup details this if you scroll down a bit. Then you just plug your ouya in with a normal micro-usb cable for a phone into your laptop and type the command
Code:
adb reboot recovery
You'll need a keyboard from then on to navigate the recovery menus.

Hope this helps you!