I assume that you can run a CAT 5e cable from your main router (one of its LAN ports to an LAN port on the WRT120). Assign the WRT120N a static IP address that is outside of DHCP assignment range of your main router but still in the same network.
Next shut off the DHCP server in the WRT120N your main router will be assigning IP addresses so the one in the WRT120N must be disabled. The WRT120 should also be using the same SSID name as the main router.
After setting this up you can connect the WRT120 to your network and have it work as an access point. It is also better if you use two different radio channels on the main router and the access point you can change those in the wireless configuration of the WRT120.
Your AP security should be the same as your main router and use the same passphrase.
So for example if your main gateway router is 192.168.0.1 allow it to assign addresses in the range of 192.168.0.2 - 192.168.0.75 and make your WRT120 address 192.168.0.76. All subnet mask settings would be 255.255.255.0.
You need to set them up as WDS repeating (if they are compatible) this will allow your wife to wirelessly access the AP transparently.
Otherwise you may need to DD-WRT the spare router however I dont think the WRT120 is supported check out DD-WRT.com for more info.
WDS allows for Bridging and Repeating Bridging simply "bridges" two separate networks while Repeating makes one of the participating routers to function as an extension of the main router like an access point.
Just expands coverage which is what you want you do not want bridging.
If you have Linksys WRT120N router manual then you can find appropriate instructions from there. But don’t worry if you don’t have that.
Let’s begin the main process -
Step 1 : First of all, you have to connect your computer to LAN port of router through an ethernet cable.
Step 2 : Once Linksys router assigns an IP address to your PC, you need to access the web-based setup page of Linksys router. Normally, you can access Linksys router web page by entering 192.168.0.1 or 192.168.1.1.
Step 3 : After that, you need to log in using username and password. The username and password entry will be “admin”. Don’t confuse between them.
Step 4 : Once you access the settings page, there will be a guide that will take you through configuring the Linksys router.
Just check these points -