Does the PC have to be on for your other devices to have internet access?
If so, it sounds to me now as though the Wi-Fi on your wired Windows 8 PC is the access point for all your other Wi-Fi devices. Don't do that.
Look in the router's configuration screens, what devices are connected to the router? I'm guessing you'll find only the PC is connected to the router, possibly one Wi-Fi connection, possibly a Wi-Fi and a wired connection.
If there's only a PC Wi-Fi connection, create a wired connection for the PC so there will be two PC connections to the router.
Turn off the PC's Wi-Fi on the PC, not the router.
Next check to see that the PC still has internet access through it's wired connection, it should.
Next check your other devices for internet access, if my guess is correct, they won't.
Get the other devices back on the internet through the router's Wi-Fi, do not switch the PC's Wi-Fi back on to do this.
Now try the EOS Utility, hopefully you can connect the PC to the camera through the router without borking the rest of the network, test and see.
If the network borks with the EOS Utility running, turn on the PC's Wi-Fi, delete all connections to other devices through the PC's Wi-Fi, use the PC's Wi-Fi only for the EOS Utility.
I'm guessing now, and only guessing, that you shouldn't need the PC's Wi-Fi to use the EOS Utility, but you might find that you have to.
Don't know about AirPort routers, but with others I've worked with, a wired connection to the router is essential for the initial router setup, setting up passwords and such, once passwords are configured, Wi-Fi devices can then connect to and through the router using those passwords.
Router changes can then be made over Wi-Fi, but some of those changes can require a wired connection to get back into the router so it's always best on such routers to always have at least one wired connection available.
On my network, the wired connection is through my old PC that hardly ever runs anymore, I only boot that machine to retrieve some file I've forgotten to transfer to my new machine, or to make lower level changes to the router.
Both of my Canon printers are Wi-Fi connected to the network through the router as well as my new PC, my Android phone and my Android tablet. I can easily and seamlessly print from either PC, the phone or the tablet to either printer, it was very easy to set up.
I use DSLRController to connect my 6D to both my phone and tablet (one or the other, not both at the same time), but I use wired tether to do so.
I've found 6D Wi-Fi seriously wanting, wired tether solid, stable and much less lag.
I briefly tried tethering the 6D with DPP and Lightroom with the PCs, tried EOS Remote with four different Android devices, found a whole lot more functionality with DSLRController so I now use that exclusively for tethering tasks, don't bother about the other choices.