How to talk to my dad about his behavior towards my dog?

The only way you can ensure that your dog does not have any contact with your father is not to leave it with him when you go somewhere. Do you still live with them? If not then don't let them watch or take care of your dog when you leave town; board the dog or have a friend watch it. If you still live with them, then the best way to avoid the dog having contact with your father is to wait until you are no longer living with him. He seems set in his ways, but I would not bring a dog into that household.