His car hit a hole that contained a mine and his daughter and wife died

Firstly: 

We ask Allaah to reward you for your calamity and to compensate you with something better; and we ask Him to purify the land of Iraq — and all the Muslim lands — of sinful aggressors and to grant victory to His close friends and to humiliate His enemies, for He is able to do that. 

Secondly: 

If you were driving at a speed at which you were able to control the car and you were not able to avoid this hole, then there is no blame on you because you were not negligent, and you do not have to offer expiation or pay blood money. 

But if you were driving at excessive speed, at which you could not control the car, then you have to offer two counts of blood money and two expiations for accidental killing of your wife and daughter, because you made a mistake and caused their death.  

The main issue is whether or not you were negligent, and negligence may mean excessive speed, not paying attention to the state of your brakes and tires, staying up too late and not sleeping, and other things that may have been the cause of the accident. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in his essay Ahkaam Hawaadith al-Sayyaaraat: If the driver of the car does something intending to escape danger, for example if he is faced with something that he fears will harm him in a crash, or someone comes out from the right or the left in such a way that he cannot stop, so he swerves to avoid danger and an accident occurs, or he suddenly sees a deep hole in front of him and he swerves to avoid it and an accident occurs — in these cases there are no consequences such as requiring expiation or compensation, because he acted responsibly and did what was required of him of trying to avoid danger, so he is in the right  and “No ground (of complaint) can there be against the Muhsinoon (good-doers)” [al-Tawbah 9:91]. 

Thirdly: 

If there was negligence, then the one who was negligent is obliged to do two things: to pay blood money and offer expiation for each one who died. But if the heirs waive the blood money, he is no longer obliged to pay it; as for expiation, it cannot be waived. 

The heirs do not have the right to waive the blood money if the slain person owed debts or if he has heirs who are minors; rather his debts should be paid from the blood money. An heir who is an adult of sound mind may give up his share of the blood money if he wishes, but for the minors their share remains due. See: al-Sharh al-Mumti’ (11/321): 

The expiation for killing is freeing a slave; if that is not possible then it is to fast two consecutive months, because Allaah says (interpretation of the meaning): “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.” Then He says:  “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 Allaah” [al-Nisa’ 4:92].