Your existing switch should work. I have a 100mbps switch that serves the wired equipment in my home and it works fine to connect a Hopper to Joeys. A separate network is not required.
I can then jack the Hoppers into my gigabit network. Then I can locate any Joey in any room where I can jack it into my network. Are we sure this does not have to be connected through its own switch.
We even have one user on our site who is using a wi-fi dongle on a Joey to connect it to his home network.
The caveat is that Ethernet is not officially supported. If it doesn't work don't expect DISH to try to fix it for you.