How to "share" WiFi

My dad was recently transferred across the US and is living in an extended stay hotel. He has WiFi but it requires you to log in before you can use the internet, so his 3DS and Xbox 360 won't connect. I hoped that we could make an ad-hoc network from his computer, but first: the 3DS only recognizes infrastructure networks, and B: he has no Ethernet hookups in his suite.

If his phone is hooked up to the WiFi, is it possible to use the hotspot feature to share it; or will that only work with a cellular signal? Does anyone have any ideas or suggestions that would let him get internet access on his 3DS and Xbox 360?

If you have a laptop and a usb wireless adapter, you can create an ad hoc network using the usb NIC and bridge your hotel wifi connection (connected to the laptop's built in nic) over to it, thus creating a sort of wifi hub on your laptop/usbNIC setup to connect other devices to.

I'm not sure about the phone however, but in order to broadcast wifi a device needs to make use of its NIC to either connect, or broadcast, not both. You can tether wifi via cellular connection due to them both using different antennas. Likewise a standard laptop with only its built in NIC can't broadcast a network while being connected to one.

USB nics can be bought at walmart/target though for about $30-40 and could accomplish what you want.

Nope
You can't connect to the wifi and run as an access point at the same time.
Though you could use 3g/4g and run a hotspot.

Is there a way to make this recognizable by a gaming system? I know that it's basically the same as sharing an ethernet connection and that doesn't work. I've heard of a program called Connectify, but I don't know if the lite version will suffice. Does anyone know?

is your 360 the newer variant with wifi? Also, this technique with an extra usb nic doesn't require a wired connection from the computer to the hotel.

Another idea is to connect the laptop using wifi then connect the 360 via ethernet to the laptop, and bridge your connection over to the ethernet connection.

Yeah, it's the new 360 so I know that will work. My main concern is the 3DS, I had bought my dad Mario Kart 7 so we could play together and I'd really like to get that working.

an ad hoc network can be broadcasted with whatever encryption you want, your 3ds can connect to wep, wpa/wpa2 from wifi just fine

Unfortunately, as I said in the OP the 3DS wont with ad-hoc. Hence my need to find a work around. I'd bet that if the 360 can connect the 3DS should be able to as well; but I don't have the 360 to test with or a USB NIC either. I will try to setup my computer with connectify. If I use the Ethernet as the internet source and broadcast a wifi network do I need to share the Ethernet or the wifi?

You can use connectify to share the ethernet connection over a usb nic/internal nic if you're running through cable. consoles can connect to the hotspot like that, I've done it with a vita before since it didn't support my college's wpa2 enterprise.