It may not be relevant, but I had a lot of trouble trying to use an AEX and AppleTV simultaneously (gory details
here).
To save you the bother of reading it all, I couldn't use the AEX if I was streaming a movie to the ATV, and with much help from bosie we eventually isolated it to some sort of oddity in my 3Com router. I haven't cured it, I just live with it
It could be the same sort of thing- the router doesn't like connecting to iTunes radio whilst streaming to the AEX.
Is it OK on the internal speakers?