If you pull it out on the dog you better have to use it. I don't think the dog is going to see your gun and go "Oh [color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color]" and stop.
Anyway, I would have stopped dead in my tracks and seen how far the other dog was going to get and held my dog tight. If the cable broke and the dog charged I would have released my dog to intercept hopefully giving the young girl time to get away, who knows if the other dog would go after her instead, right. If there was a good length left of the other dogs cable, as the two dogs were fighting I would grab the end of it and tie it to the nearest secure object, then grabbed my dogs leash and dragged him away from the fight as hard as I could. If I had no other choice I would have to put down the other dog and deal with whatever happened when the police showed up.