I have purchased three Airport Extreme routers. I have a cable modem in one room that currently feeds into our primary router (which I want to replace with an Extreme), which feeds into a switch, which then distributes Internet and LAN services over ethernet via CAT5 to an office upstairs and another office a few rooms over. (The walls in our building are thick, so I can't do a purely wireless mesh.)
What I want is basically for one Extreme (the one next to the cable modem) to be my primary router and DHCP server, and the other two to be access points extending the primary network.
I tried using the Airport Utility to set it up following their instructions to extend a network, however, it seems that it was trying to do so wirelessly, not through the ethernet cables I had plugged into the Extremes. As a result, the two access point Extremes kept losing their connections to the primary Extreme.
How can I get this setup to work the way I want it to?