Can I daisy chain AirPort routers?
No, not using wireless only.
That's because Apple's extend a wireless network feature works like the hub and spokes of a wheel. In your case, the AirPort Extreme is the "hub" and the AirPort Express would be a "remote" located at the end of a "spoke".
It's possible to have multiple "remotes", but each device would reside at the end of a "spoke" and as such, it communicates directly to the "hub".....not to another "remote" at the end of another "spoke".
The perfect setup in most homes would have the "hub" centrally located and the "remotes" would reside at the outer portions of the home. Few of us are so lucky to have a "hub" located this way though.
Is there a signal enhancer available that could pass the signal through the interfering walls?
Unfortunately, no. As you probably know, the wireless signal power of all routers is limited by law...and WiFi signals just don't pass though obstructions very well. Of course, the signal will penetrate a wall board wall a lot more effectively than a dense wall of cement.
The bottom line here is that if it is always better to connect remote AirPorts back to the main Airport using a wired Ethernet connection. This allows you to locate the remote AirPorts exactly where they are needed to provide the best signal coverage in a given area.
If you cannot run the Ethernet cable, then sometimes Ethernet powerline adapters can be used to send an Ethernet signal over the existing AC wiring in your home.
The theory here is that you already have the wiring in place, you just need the adapters. In practice, things sometimes do not work according to theory though, so some experimentation may be needed if you decide to try the powerline adapters. Understanding the store's return policy in advance might be a wise thing to do.
