From what I understand, the airport express can't receive G1100 signal via wireless like it could with the airport extreme?
It appears that you may be confused or have received some incorrect information.
The AirPort Express can "join" the WiFi network of virtually any 3rd party router for use with AirPlay. My neighbor is using a Fios router and has no trouble with his two AirPort Express devices joining the Fios WiFi network.
A guess would be that you might be thinking of the special feature that the AirPort Express has to "extend" a WiFi network. The Express can only "extend" the WiFi signal from another Apple AirPort WiFi router.
If you want the AirPort Express to join the G1100 WiFi network, you will need to reset the Express back to factory default settings and then set it up again. Apple's set up "wizard" will suggest the correct settings for the Express to "join" the WiFi network there.
In the example below, you can see that the AirPort Express is being setup to join a WiFi network that is named "2Wire902" provided by an ATT router. You will see the name of the G1100 WiFi network on your screen.
To reset the AirPort Express......
Power it up and let it run for a minute or two
Hold in the reset button on the back of the Express for 7-8 seconds, then release
Allow a full minute for the Express to restart to a slow blinking amber light status
On your MacMini.......
Click on the WiFi menu at the top of the Mac's screen
Look for a listing of New AirPort Base Station
Click directly on AirPort Express
When you click on AirPort Express, that will start up the AirPort Utility setup "wizard". The wizard will take a few seconds to analyze the network and then display a screen that is similar to example above
Type in a name that you want to call the AirPort Express
Type in the password for the G1100 network
Type in the password for the G1100 network again to confirm
Click Next
The wizard will configure the AirPort Express for you
