Custody of the children should not be given to a kaafir. This is the view of Maalik, al-Shaafa’i and Ahmad. (al-Mughni, 11/412). If the Muslim relatives of the man are far away, then the children should be sent to them. If that is not possible then the children should be given to a Muslim family to take care of them and have custody of them. 

The conditions of custody include the following: 

Being Muslim, for custody cannot be given to a kaafir. 

Being of sound mind, for custody cannot be given to one who is insane or mentally deficient. 

Being an adult, for custody cannot be given to a minor. 

Being able to bring them up properly, for custody cannot be given to one who will be negligent. 

Ibn al-Qayyim said: 

No custody can be given to a kaafir over a Muslim for two reasons: 

1 – The one who is given custody of a child will be keen to bring him up in his religion and to teach him about it, and after he grows up it will be difficult for him to change. He may change him from the natural disposition of man with which Allaah has created His slaves, and after that he may never come back to it, as the Prophet (peace and blessings of Allaah be upon him) said: “Every child is born in a state of fitrah (natural disposition of man), then his parents make him into a Jew or a Christian or a Magian.” There is no guarantee that the one who has custody will not turn a Muslim child into a Jew or Christian. 

If it is said that the hadeeth only applies to the parents, we should say that the hadeeth refers to the usual situation, which is that a child usually grows up with his parents, but if one or both are lost, then the child’s guardian among his relatives takes their place. 

2 – Allaah has severed the ties of closeness between Muslims and kaafirs, and has made the Muslims the close friends of one another, and the kaafirs the close friends of one another. Custody is one of the strongest reasons for creating close bonds, which Allaah has severed between the two groups. 

Zaad al-Ma’aad, 5/459. 

And Allaah knows best.