if "could not have driven" is used to mean "wouldn't have been able to
drive" what is the exact meaning of "could not have been able to drive
her"? Could you please rephrase it? –
I wanted to put this in a comment, but my response would be too long. It is hard to explain these forms without using the very forms I am trying to explain and being circular.
As you are probably aware, English 'helping" verbs have different meanings and nuances. Some of these meanings also vary by tense. "Can" is often the equivalent of "be able to" or "to be possible for someone to do or be something."
The verb "can" has one other form "could." This form can represent the simple past tense of "can" (i.e., "was able to") or the conditional tense of 'can" (i.e., "would be able to") As a result, a sentence like "he could drive" is ambiguous.
If you are referring to a past situation, then "he could drive" is generally understood as as statement of past ability or past possibility (e.g., "he could drive at the age of 18"). If you are referring to a present situation, then "he could drive" is generally understood as representing something in the present that will prove to be true depending on some other conditions ("he could drive there now if the roads are clear.").
The conditional usage of "could" is also used to express your assessment of what is true based on what you think. The truth of the statement is conditioned not so much on the facts directly, but the correctness of your assessment of the facts. For example, "He could be lying to us with all his claims, but I'm not sure."
In addition to changing the form of "can" to "could," you can also change the form of the verb it is used with from a present form to a past form (e.g. "he can drive" can be changed to "he could have driven."). These transformations interact in complex ways.
The form "he could not have driven" is also ambiguous, but for some of the reasons stated above.
If you want to talk about a conditional ability or possibility in the past, you need a past conditional form of "can"/"could," but none exists for this verb. Instead, you make the infinitive it accompanies in the past tense form (i.e., the perfect infinitive). In that case, "he could not have driven" is the equivalent of "he would not have been able to drive." What makes "can" conditional are the facts that were true at the time.
If, however, "he could" refers to your present assessment, you do not want to put replace "could" with a past tense form, since your assessment is in the present. Instead, you add the past infinitive to express that your present assessment is about a past event. In this case, "he could have driven" means: "I assess under the circumstance that he did drive." What "can" is conditioned on is not the facts, but the correctness of your assessment. For example, "he could have being lying to us, because what he said doesn't seem to be true." This does not address his ability to lie given the facts, but rather your assessment ow whether he was indeed lying given the facts.
If you say "he could not have been able to drive her," using both "could" and "able" in the same phrase, you cannot be talking only about a past possibility or ability. Here, "could" can only be a present assessment of a past ability drive. You are saying that the truth of whether or not he drove her depends on whether your assessment of his past ability is correct. In other words, you deduce that he it is not possible that he had the ability to drive her.
In summary, "he could not have driven her" could refer to his inability to drive her at that time or to your assessment that he it is not possible that he drove her given the facts you know. If you say, "he could not have been able to have driven her," this disambiguates the meanings and can only be understood as your deduction about what facts are true. This sentence is also very "awkward" and is less likely to be said than the first alternative which tends to have the same pragmatic meaning. You would say the last sentence only if there was a strong emphases on what ability he had to drive.
