I figured out a solution! Basically, instead of running YouTube from the Bluetooth option, turn the Pandora option on and the audio will begin to stream from YouTube.
I'm having the exact same issue in my 2015 mazda6 touring and my iphone 5s with ios 7.1.2. YouTube goes on for a second and then pauses. If I try to unpause it by selecting play/pause, my ipod music starts playing. If I try to get YouTube on again, it won't stream the sound.
I brought it to the...