Is there an option in Windows 7 (or 3rd party) to offer Tethering (that is, act as a WiFi hotspot while being connected to a WiFi network?)
Take a look at Connectify: http://connectify.me
A detailed step-by-step to setup wifi tethering/hotspot in Windows 7, Windows 8 WITHOUT any 3rd party software:
From admin Command Prompt type:
netsh wlan set hostednetwork mode=allow ssid=mywifinetwork key=mysecretkey
Enable new virtual Wi-Fi adapter (it might be disabled upon creation)
From admin command prompt type:
netsh wlan start hostednetwork
From current internet conection adapter share (ICS) internet to the new virtual adapter
Connect from wireless client to virtual SSID. Wi-Fi client gets an auto IP and you're good to go.
After host computer restart you only need to repeat steps 3 & 5 to be up and running.
Create an ad-hoc network. Here is the guide for Windows 7 from the Microsoft site. http://windows.microsoft.com/en-US/windows-vista/Set-up-a-computer-to-computer-ad-hoc-network
You could use the ad-supported Connectify app, as someone else mentioned, or use http://virtualrouter.codeplex.com/, or do it my hand with the netsh command and ICS with a little bit of effort:
netsh wlan set hostednetwork mode=allow ssid=YOURFRIENDLYSSID key=SOMEPASSWORD netsh wlan start hostednetwork
... then share the real connection through the virtual WiFi NIC.