When is could too repetitive?

I am having trouble figuring out when to use the word, could.

For example, in the sentence "There is a possibility that person had hit my car". If I used "could have" instead of "had", I think it would be repetitive.

But in the sentence, "There is a possibility I could have done better". Without the could the sentence meaning changes.

In your example, swapping "had" for "could have" would change the meaning of the sentence.

"There is a possibility that person had hit my car". Means: your car was hit (by someone), and it is possible that it was "that person".

"There is a possibility that person could have hit my car". Means: your car was not hit, but if the conditions were different, then "that person" might have bumped into it.