You can treat mange at home but it's a good idea to get the skin scraped to find out what type of mange your dog has. If it's been passed along to the other dog it could be Sarcoptic Mange, or Cheyletiella Mange also known as walking dandruff. Typically Demodectic Mange is only passed along from mother to pup. So if both your dog's have it I would assume they would have either Sarcoptic Mange or Cheyletiella Mange which are both highly contagious. If the issue is treated early on and not left untreated for any length of time typically recovery is very good. But you really need to have a skin scrap done to confirm that what the dog's have is in fact manage. As far as the surgery is concerned I would hold off until you get this under control especially if they have Sarcoptic mange. And yes Sarcoptic mange CAN be passed to humans! So if that's what your dog's have you will need to be treated as well.