I am trying to set up multiple Apple TVs to stream movies from an iTunes movie server, as well as allow Airplay connections. The problem, I think, is that each Apple TV is on a different network. They're connected with Ethernet. I have attached a carefully drawn diagram of how it is setup currently.

The second wireless network exists to serve a room which the main network can't reach very well, due to distance and thickness of walls. If I'm Airplaying to the TV in that room (or connecting to the internet) I need to connect to the secondary wireless network.
Currently Apple TV (a) works just fine. It can stream the iTunes movies and, when an iPad (etc) is connected to the main wireless network, it can Airplay. However, if I connect an iPad to the secondary wireless network it cannot Airplay to Apple TV (a) - not a big deal I guess.
Apple TV (b) cannot see the iTunes movies. It just tells me to turn on Home Sharing. I can Airplay to it if my iPad is connected to the secondary wireless network, but not if it's connected to the main network.
I have a 3rd Apple TV to add in, but not until I sort out the first two!
All devices are using the same Apple ID.
I wondered if adding in a switch like this one between the main and secondary wireless networks would help, with the Apple TV (b) connected to the switch? But I don't think that would help the Airplay issue?