|Ok, well, your design is the right way to set it up then.|
internet >> Router >> Server >> Switch >> Clients (wireless/wired)
Personally, I would do the monitoring with another device in order to reduce the load on the DC. It's always a good idea to keep the load on your DC's to a minimum, especially when it's your DNS server and likely your DHCP server as well.
On a side note, do yourself a favor and create a redundant DC.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.