... I set up the Express as "extend a network;" I entered the Apple ID of the Extreme on the WDS screen.
Ah. I am glad you told me that. As I understand your network, you want the Express to "create a wireless network", not "extend", "join", or "participate in a WDS".
Create. The network it creates should have the *exact same network name and security* as the network you instructed your Extreme to create. Leave its radio channel on "automatic" though, since the Express and Extreme will need to use
different wireless channels. "Automatic" will let them figure that out between themselves (though you should confirm they're really different after they've done so).
Under "internet" make sure "Connect Using" is set to
"Ethernet". "Connection Sharing" must be set to *"off (bridge mode)"*.
The fact your Express is connected to the Extreme via Ethernet is a very good thing. In that configuration, your Express will get its IP address from your Extreme via Ethernet, and create its own wireless network. Your computers can wander from the Extreme's wireless range to the Express's without interruption.
A WDS accomplishes the same thing, but without a wired connection between the two base stations. In that case you would need both radio channels to be identical. Since they're connected via Ethernet, you don't need or want a WDS. It's a pain to set up and presents significant disadvantages over the wired connection that you have.
You can leave the Extreme's "allow this network to be extended" check box set, or not. It won't hurt anything but that's not what you need in this configuration.
I'm not using an Airport network at the time being, so there might be something I missed until I can verify these steps. Until then I hope this gets things going in the right direction.
