How should i approach my father about his behavior towards dogs?

This is a problem with your parents, your father particularly. Maybe he is addressing problems he feels with you through your dog. In other words, he can't abuse you so he abuses your dog. I don't think you will ever be able to change anything. For your mothers sake leave your dog at home or find a good boarder for when you will be visiting. Your father obviously is not going to change, he may have mental problems an dyou are not a psychiatrist. Please don't involve an innocent dog in this.