If I run over your child, I might be prosecuted if the police can prove I was drunk or driving dangerously. You could try sueing me, but I haven't got enough for you to recover your legal costs.
When the self-driving car made by a large multi-national corporation runs over your child, you will be rapidly surrounded by lawyers desperate to represent you as you try to claim your millions. Even if the child runs out in front of you, they will claim that a human could have anticipated it, and therefore the self-driving car should have.
If the self-driving car does anticipate it and brake in time to miss the child, the driver of the car behind will sue for whiplash when he runs into the back of you.
It will be a field day for lawyers when machines made by deep-pocketed corporations are responsible for decisions, as opposed to fallible and poor humans.