Question

On the longest day of my life, I had to tell my dad about wrecking his car.

run-on.
correct.
fragment.

Answer 1

On the longest day of my life by itself would be a fragment. It's not possible for this sentence to be a run on because it is not two complete sentences. So it is correct as it is written.

Answer 2

run on because it's a ongoing you had to tell dad you are k your car