The best Apple TV / YouTube Airplay solution that I have found is using the web version of Apple TV in Safari. Add a link to your home screen and you will have a nice YouTube icon on your iPhone.
Do not install the YouTube app so that your player will default to the iPhone's native player, which plays on AirPlay.
Enjoy.
Do not install the YouTube app so that your player will default to the iPhone's native player, which plays on AirPlay.
Enjoy.