Hello,
Due to the security and (Wi-Fi/Bluetooth) wireless overhead of AirPlay, you probably won't ever get the audio and video to sync when watching the video on the iPad and audio through your system. The video plays directly on the iPad, but the audio sent via AirPlay has to negotiate the connection to the AirPlay device, and the Wi-Fi/Bluetooth overhead adds to the delay. If you were to AirPlay both audio and video to say an tv, then through your system, it should stay in sync.
Hope that helps.
C