So are you mixing down two audio channels down to a single channel for broadcast? Why not get an inexpensive mixer (Really cheap, Kinda Cheap, Best low cost) to combine your signals and then push it into your sound card. The fact that you are using a sound card as your interface device hurts the audiophile in me. Use a usb interface like this instead.
You can then use some adapters to get the correct plug connections.
You should go this route because computers can only really use one audio device at a time. Technically, you can get multiple devices installed and working, but it's a real pain to do. I always like going with solutions that are designed to solve my problem instead of hacking stuff together to make something that kinda works.
Hope that helps