Well, just imagine what a relief it'll be after you go there and get the job. I am a stutterer myself and when I do presentations in uni, I kinda just live till that moment when I have to present. I feel anxious even a few days before. And I always stutter more or less. But it helps me to think that this presentation is not big of deal and the feeling that I get after I present is like lifting a weight of my chest. It's like a treat after you speak. And maybe it's not a good way of dealing with speeches, interviews, etc., I don't think you should be dependant on these "treats" but in the other hand it makes me want to speak. As much a parents are these saint things, they're not always right and you shouldn't take them seriously about your stutter. It's hard, but you will show them that you're a self sufficient person. Maybe your dad will change his mind about stuttering. Just keep going, and good luck with the interview