Networking – collect wireless packets using Wireshark while being connected to the Internet via cable

Look at Wi-Fi (WLAN, IEEE 802.11) on the Wireshark Wiki page.

See the CaptureSetup/WLAN page for instructions how to capture from WLAN's (including monitor mode), and see the CaptureSetup page for general information on capturing on WLAN's and other media.

Going further, if you are using Windows (are you?)

Capturing WLAN traffic on Windows depends on WinPcap and on the underlying network adapters and drivers. Unfortunately, most drivers/adapters support neither monitor mode, nor seeing 802.11 headers when capturing, nor capturing non-data frames.

Promiscuous mode can be set; unfortunately, it's often crippled. In this mode many drivers don't supply packets at all, or don't supply packets sent by the host.
If you experience any problems capturing packets on WLANs, try to switch promiscuous mode off. In this case you will have to capture traffic on the host you're interested in.

The AirPcap adapters from CACE Technologies allow full raw 802.11 captures under Windows, including radiotap information.

Here is another reference you might want to read up.
A Quick Intro to Sniffers:
^{Wireshark/Ethereal, ARPSpoof, Ettercap, ARP poisoning and other niceties.}

The router is a bit of a red-herring in the question as it is unlikely to have the ability to mirror the wifi data out to your PC. The best you could do with the router would probably be to put your PC between the router and the internet and sniff that traffic, but you would miss out on any traffic that stayed within the LAN.

A better approach might be to feed Wireshark the wifi passphrase and let it decrypt over the air. A guide to that is here:

http://wiki.wireshark.org/HowToDecrypt802.11