I'm not prepared to call it a mistake. He knowingly and intentionally stole a car, and drove drunk, choices which resulted in the death of his friend. That's not a mistake, an error of that sort of magnitude. It is a crime.
He intended to steal the car, he knowingly drove under the (considerable) influence of alcohol. He did not foresee or intend the death of his friend.
Regardless of whether one thinks the time was sufficient, for the crime, that was what he was sentenced to, and that's what he has done.
Neither of these two bells can be unrung.
I hope very much he does get some counselling, and maybe assistance in creating a life plan, which will have to take into account the life altering effects of having committed such a crime, having a criminal conviction, and having served a reasonably substantial (in terms of having to be declared to potential employers, etc) criminal sentence. Because he does have to live, and it's better for society if he can live a productive and constructive life, as well as for his daughter.
The number one thing that should inform your thoughts and actions OP, is the best interests of your daughter. Not her father, not you, not her grandfather. Make sure that is the question you ask yourself throughout, 'what's best for my daughter, is this in her best interests?' If he is no longer the angry, wilful drunken boy who committed the crime, if he has grown up and matured and gained some personal insight and self control, then that might be to facilitate a relationship with her father.