The newest updates to iOS and AppleTV are supposed to allow a peer-to-peer connection, one that does not require that both devices be on the same wi-fi network. But you probably need one of the newer iPads to take advantage of that: iPad Air or newer.
Do yu have a link for this as having a hard time finding it. I must admit it was 3:30 am in morning my time. Lol
I did find this however after drinking 2 cups of coffee
Peer-to-peer AirPlay discovery and playback.
With iOS 8, you can wirelessly connect iPad, iPhone or iPod touch to Apple TV without first connecting to the organisation’s network. Which means you can present or share your work even if you’re offline or the organisation has a complex network.
A faster way for friends to wirelessly connect to your Apple TV.
Peer-to-peer AirPlay lets visitors to your home or office quickly and easily connect their Mac or iOS device to your Apple TV without gaining passwords and connecting to the Wi-Fi network. Apple TV detects their device and makes the connection. So they can show off photos, share documents, stream movies, or play music right on your TV. Simple as that.
Peer-to-peer AirPlay requires a Mac device (2012 or later) running OS X 10.10 or an iOS device (2012 or later) running iOS 8 and an Apple TV third-generation rev A (model A1469) running Apple TV software 7.0.
Look for model number on bottom of the Apple TV
Hope that helps