So sorry for the loss of your dog, and for the added grief the mistake has given you
As others have suggested, I would seek a full refund of the cost-they did not provide you with the service that you paid them for. I agree with BenMax that suing might just make this ordeal even worse. Get a refund, and try to find another way to help with closure. Even just going to Buddy's favourite places and saying a goodbye might help. If you need something physical, you can always print a couple of pictures of him and burn those and then spread those ashes. I know it is not the same but sometimes things like that can help.