The internal drive I think should definitely work. Go to Time Machine's preferences, then click on the "Select Disk" button and choose the networked drive you want the backup stored on.
I've never tried to back up something indirectly via TM, and by a quick look at the preferences, I don't think this is possible.
Maybe I don't understand what you're trying to do, but why do you have to back up the networked computer via yours? Any reason you can't just set it up from the other computer itself? Seems like that'd be simpler, and as long as you still can access the backup via the network, I can't think of any obvious disadvantages...
I'm not really familiar with other backup software than time machine - it meets all my needs quite nicely. Sorry.