Airplay won't work through one of my Wi-Fi Networks

I'm trying to use Airplay and have an AppleTV and an iPhone 4S. The way my home network is set up is I have the main Wi-Fi network which is connected to my cable modem and is using an Airport Base Station Extreme. I have an additional home network which is in another part of the house where the AEBS does not work as well. That network is running on a Cisco/Linksys E3000.

The problem is if I connect both the Apple TV and my iPhone to the main network using the AEBS Airplay works fine. If I connect both devices to the other Wi-Fi network it doesn't work. I had the idea that as long as both devices are on the same Wi-Fi network it should work fine so this puzzles me. Since the Linksys E3000 network is stronger in that part of the house I would prefer to use that Wi-Fi network on the AppleTV and the iPhone.

Does Airplay require a AEBS? I had the idea it should work on any router.

Is there something I have to change in the settings for the E3000 to have it work with Airplay?

Thanks for your help.

AirPlay will function fine on any network. So that's not the issue.

Are both networks completely distinct? Different SSIDs? Different channels?

Yes, both are distinct. My 2nd router, the Cisco/Linksys E3000 is plugged into a Gigabit hub and that Gigabit hub is connected by wire to the AEBS that's in the basement of the house. The way it is set up is they are treated as two distinct networks. For example I have a printer that's hooked to the AEBS and any computer connected to the AEBS can see and print to it but computers connected to the Linksys E3000 can't see it. I would say this is what's causing the problem but yet if both the AppleTV and iPhone are connected to the E3000 it seems that even though it is distinct from the AEBS that it would not cause a problem.
Someone suggested that i do a firmware update of the E3000 so if one is available i will but I'm not sure if that would solve the problem.

Sorry, you say they are distinct. By which I meant separate. But then you go on to say they that both routers are connected by cable.
That being the case it's just one network. Which router is handling DHCP? Have you disabled DHCP on the other?