I have played two different channels simultaneously on the same premium account by using SiriusXMStreamer. Works fine that way.
From one computer, run the SiriusXMStreamer server. You can play channels directly from the program on that computer. On the other computer, access Sirius through the URLs that SiriusXMStreamer generates. Those will play just fine in Windows Media Player or just about anything else. The easiest way to accomplish that is to generate a playlist with the program and then just take that over to the other computer and import it into WMP, or winamp, or whatever.
And besides, this is SO much better than the sirius.com player. It's faster, you get logged in automatically, and you never get nagged with "are you still listening?"
Get it here.
http://www.permanence.com/sirius/