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I would love to have someone to look up to, to follow, to learn from, to model my life after, and to be proud of me. But I can’t help feeling like my dad is not that person. I feel like I just don’t really have a good model in my life that I can follow, and it’s affecting all aspects of my life, particularly my faith.
... regardless of who is right or wrong, try to respect your dad for who he is.
Have you talked to the person who knows your dad better than anyone else in the world, your mom, about any of this? Obviously, it depends on the situation, but while it's something you and your dad should resolve between the two of you, your mom would probably be a good person to go to for advice. Since you didn't mention her, I assume that your relationship with her is better? Either way, I'll be praying.
Have you tried to do something fun with your dad or just have a time with you and him?
Prayer is awesome but that doesn't mean you are a bump on the log and do nothing. You said that you both spend a lot of time in your rooms, why not take some time to spend some time in his room?