I put a young dog to sleep years ago. The dog wasn't "right." The vet wholeheartedly supported the decision. I agonized for weeks. It came down to what was best for the dog and his quality of life. I was there for this rescued stray at the end.....it was the best I could do.
Your wife is scared of the dog with good reason. Her emotional well being might be more important than 'saving' a dog.
I wish you the very best whatever happens. Please ensure this dog doesn't connect with a person. If he goes for the throat he could kill someone.