We have two small switches that do not broadcast DHCP numbers
OK, sounds like you're confusing your terms. I can guarantee you that your switches
do 'broadcast DHCP numbers' because broadcasts are how the client requests a DHCP address and fundamental to how the DHCP protocol works.
What you want is a device that
issues DHCP numbers - in other words a DHCP server. Completely different thing. Not all routers are DHCP servers.
We need a very small router for these machines so they can be on a seperate LAN gig-e network that we can transfer our huge video files on
Sounds like you need a switch more than a router.
... I set up our Xserve to broadcast a DCHP number (172.xxx.x.x) so I could set up the gig e network and when I did this, it broadcast the IP number to our 192.xxx.xxx.x.x network
Then your network design is at fault.
You shouldn't try to run multiple DHCP servers on the same LAN. Since DHCP uses broadcast for discovery/address assignment you
will run into problems with machines getting a DHCP address from the server you don't expect.
There are ways of running multiple DHCP servers on a LAN but it takes work and should generally be avoided if possible.
What I need is some advice on a type of inexpensive router that will be able to do this
Given what you've said it's absolutely clear that you do not need a router. You don't need anything more than a switch. You might even be able to use your existing switch if it supports VLANs.
Given the small number of machines, it's not even clear that you need DHCP either - you could just configure all these machines manually, using statically-assigned 172.16.x.x addresses.
If you do want to use DHCP, the XServe can certainly do this without leaking into the 192.168.x.x network - it's just a matter of configuration.
Assuming you want to use DHCP, your XServe has two ethernet ports. One should be connected to the 192.168.x.x network and you should configure the second one in the 172.16.x.x network.
Using Server Admin you can enable DHCP to hand out 172.16.x.x addresses on the 172.16.x.x interface (this will prevent the XServe from leaking 172.16.x.x addresses into you 192.168.x.x network.
Now all you need to do is connect the second port on the XServe (172.16.x.x) to a switch that's separate from your existing switches (or to a separate VLAN on your existing switch if you switch supports VLANs), then connect each other device to this same switch (or VLAN). Given that you have 9 machines that need to be in this 172.16.x.x network, any
16-port gigabit switch will do the job.