Is it permissible to use the financial sum that the father of the deceased insisted on offering for the funeral arrangements, after the mother of the deceased refused it, for a charitable project on behalf of the deceased?

If the mother waives her right to the blood money (diyya), the right of the other heirs does not fall, and they can claim their rights. If all adult heirs agree, they may place the blood money in a charitable project or an ongoing charity (sadaqah jariyah) for the deceased. If not all agree, then it applies only to the share of those adults who consent to it. If the accident occurred after the driver took precautions and did not violate traffic laws, then there is no blood money owed by him, and no sin. If the blood money is not established, there is no objection to taking a condolence sum and spending it on the aforementioned charitable causes, provided that this is specific to those adults who consent to it.