I used to have my network as you suggest - See the UK network setup section of my user page on the wiki - http://wiki.linuxmce.com/index.php/User:Techstyle
. this was mainly for ease of cable routing rather than any positive reason
However, since then I have reconfigured my Network (see the US network setup Section of my user page) and as Thom says it really does work more smoothly. I used to have problems with not being able to access media on my windows PC's on the network - windows does a terrible job of managing shares. Also whenever I reset the core it would acquire a IP address from the router that was not neccesarily the same as before therefore the webadmin page address would change from the external network and non of my favorites would work. same goes for running the web version of orbiter.
On your second point
How did you conclude it was your Core NIC not being recognized?
There are a number of possibilities - your second NIC is not compatible or is it the NIC in the media director or Media Director not having a PXE boot rom.
My knowledge of what it would say if the second NIC is not compatible is limited but I would think the table on the Network page (shown below) would be missing numbers in the eth1 section
if it isn't you could always hit the swap interfaces button and see if you have internet access on the core.
in the past I have had more trouble getting MD's to work than the second NIC in the core, but I may have been lucky.
if this doesn't help send us details of your NIC