There’s a lot of personality regarding a person’s car, so focusing a story around his dad's provides a nice emotional story here.
You may want to go thru it and look at verb tenses. The dad dying surprised me and I think it’s because of the first line: “My dad drives a 57 Chevrolet”...if I'm reading it correctly, technically, it would be “drove” if he’s telling the story in the present day.
Verse 3 is pretty concise, but maybe v2 could flow a little better by trimming a couple of those little words (“he” and “then” for example) in the beginning lines there to keep it flowing and focused on the neat details you provide and not lose any meaning. Just a thought.
The part where he’s with his boy and the car now is touching...especially, “we tinker under the hood”. I can really see that!
Kristi