Indeed it is a very difficult project dispite sounding easy.
Have you examined the sound on an oscilloscope? You will find that the signal from each channel looks quite different. For a start have you checked the phase from the two signals are the same.
Rather than a simple trigger you need to take a seriese of samples from both sources and apply a sliding correlation between the two to find the actual delay. I am not sure if the arduino is up to that due to the A/D speed you need.