I don't know everything that's gone on between you but I'm all for second chances. But pay attention to his actions rather than listening to his promises. He needs to show you things are going to change. If you see no change or after a little while he slips back to his old ways that shows you he's not willing to work things through.
there would be no harm in trying but i know how fed up you have been so maybe stick to your guns. id def put foot down on dog. he needs to concentrate on you and the kids more and put effort into yous rather than the dog. xxx