Freeing a slave and fasting as Kaffarah for involuntary manslaughter
If reality is exactly as what you have mentioned, what you did is involuntary manslaughter because you were negligent in checking what was behind your car. Accordingly, it is Wajib on you to pay the Diyah (blood money) of your daughter to her heirs unless they waive it. However, you are not entitled to inherit from her and it is Wajib on you
to make the Kaffarah (expiation) of involuntary manslaughter which is freeing a believing slave or, in case of inability to do so, observing Sawm for two successive months. It is worth mentioning that feeding or paying money to needy people is not sufficient for (Part No. 21; Page No. 275) the Kaffarah in question since Allah (Exalted be He) only mentions freeing slaves and Sawm, and your Lord is never forgetful. He (Exalted be He) says:
...and whosoever kills a believer by mistake, (it is ordained that) he must set free a believing slave and a compensation (blood-money, i.e. Diya) be given to the deceased’s family, unless they remit it.
Until His saying:
And whoso finds this (the penance of freeing a slave) beyond his means, he must fast for two consecutive months in order to seek repentance from Allâh. And Allâh is Ever All-Knowing, All-Wise.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.