You could sew or glue....if glue, get the right one and put the two halves in a vice for 24 hrs to set the glue. Seems your main problem is a dog one, not a repair one. Have some-one sit with the dog to blow a whislte or distract him when he starts to chew. Failing that, do very short distances with your dog, slowly extending but stop as soon as he starts chewing. Takes time, but is better than what you have just now.
Kew, June 2010