1. Comma after "brother": You need a comma after "brother" to separate the introductory phrase "One day my dad and his brother" from the rest of the sentence.
2. Period after "story": The phrase "stop me if you have heard this story" should be separated from the rest of the sentence. It's an interjection, so a period after "story" would be appropriate.
3. Comma after "story": You also need a comma after "story" to set off the interjection.
4. Capital letter for "started": The word "started" should be capitalized because it begins a new sentence.
5. Question mark at the end: The sentence is a question, so it needs a question mark at the end.
Corrected Sentence:
One day my dad and his brother, stop me if you have heard this story. Started out on what they thought an uneventful drive to work?
