I'm upset that my brother won't let me drive my nephew to a ball game because I got a DUI even though it was almost a year ago
I'm sorry to hear that. Do you think his decision is unreasonable?
It is unreasonable, but I can't let my feelings to get out of hand
If he does not want you to drive his son, you need to respect that decision. It is his son and he can decide how he goes to the ball game.
It's easy for you to say but I'm mad that he is doing this to me. I'm going to call him up and tell him off.
Remember, you said you didn't want your feelings to get out of hand. If you tell him off, you reaffirm his beliefs that he shouldn't trust you. Instead, respect his decision and he might change his mind in time.