Everything always goes back to morality. Do you care or not? In a logical sense it easier just forgive and remove the problem of a pestering man. People will always die. No way of preventing it. In the end its just your emotions and attachments to the decist corpses that care. So logically thinking better just to forgive and remove the problem.
Voluntary admission of wrongdoing is one of the most defining qualities in a human being, so it should definitely be accepted. Forgiveness, however, lies in the circumstances. My late great grandmother passed as a result of being struck by a car; I won't go into the details, but the driver did everything in his power to prevent it and couldn't. He sincerely apologized, and we did not press any charges.
Mistakes happen. No mistake, I'd sue the pants off of him, but at least he knew that he did wrong.
Wait, I need more words, don't I.
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In life, mistakes happen. Some worse than others, but we try to move on; but given the question, would I accept the apology of ones mistake because of his or her own accident? I would not because his or her decision ruined my life. He or she decided to be irresponsible, while on the road, and because of their mistake; impacts someones life. It is wrong, and would not accept the apology.
How can you be sure that they're really sorry? You can't expect to solve everything by just apologizing - sometimes, like in this extreme situation, an apology isn't enough to right the wrong. If a stranger was responsible for my parents' death, I'd be devastated and wouldn't just smile and forgive them. Losing your parents is a massive deal - the person responsible should do more than just apologize.
If they did everything they could to try to avoid the accident then I would forgive them. BUT if they had been irresponsible I would NOT. As for revenge I would not seek revenge unless you count legal action as seeking revenge, but I don't. Legal action is just seeing that justice be done.