Is the father accountable for anything if the car he was in with his children overturned after he fell asleep, and two of them died?

If the driver was negligent in taking safety precautions or continued driving despite feeling drowsy and tired, then he is sinful and responsible for what resulted from the accident, including expiation (kaffarah) and blood money (diyah) for each life. The blood money falls upon his 'aqilah (male relatives on his father's side), and he does not inherit from it. However, if there was no negligence or feeling of drowsiness except at the very moment the accident occurred, and prior to that, he was in normal conditions, then there is nothing upon him.