Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.

To proceed:

There is a scholarly difference regarding insurance contract. Many scholars held the view that it is an unlawful contract. A group of scholars held the view that it is permissible.
If u entered this contract not knowing that it is impermissible then there is no sin on you, consequently you have to take back what you paid to the insurance company and pay it to the family of the deceased boy. What is apparent to me is that this is the ruling if you were forced to enter into the contract.

With regards to expiation; if the accident was due to a mistake from the driver or contravening of the traffic rules then he should expiate by freeing a slave, if he cannot find a slave then by fasting for two consecutive months. He can start to fast whenever he wills. He can also choose to fast during months that have shorter days and cold weather. It is true that the expiation of killing by mistake is not obligatory immediately after killing as has been said by a group of Hanafite, Shafite and Hanbalite scholars.
And Allah knows best.

Your brother,

Dr. Khalid al-Mosleh

06 / 09 / 1424 AH