I don't think a second instance of Darkice will work because the first instance will lock the sound card and won't be usable by the second instance.
Icecast 1.X had documented a feature called Relay Push where the server would act as a source client to another Icecast server. After much hair pulling, I was informed that the feature was broken and never fixed due to lack of a perceived need. The Relay Push function did work however.
These terms appear to have vanished from Icecast 2.
From my reading on Master/Slave relay options for the Icecast 2 servers, it doesn't appear there's a way to connect Icecast as a source stream to another Icecast server without some special configuration on both machines.
If your home Icecast server is accessible from the Internet, you may want to take a look at this thread:
stream feed from my server?
From my limited experience with Icecast, it would appear that it's easier to 'pull' than it is to 'push'.
If Darkice, or some other streaming software could utilize another stream as an input, instead of a sound card, it would just be a matter of starting another instance of Darkice after the first instance has put the streams onto your home Icecast server.
My interest in this was that I was looking for a way to listen to my own stream without using download bandwidth.