Divorce is especially painful and difficult when the couple have had children, and awarding custody to either party involves difficulties. According to Western law, both father and mother have to prove to the court that they are more capable of looking after the children, and this often involves maligning the other party in order to strengthen their own claims to custody. Islamic law has its own clear decision on this issue. Custom of young boys and girls goes to the mother. The son stays with his mother until he is about seven or nine years of age, after which he is looked after by the father. The daughter remains with her mother until she gets married. The exception is when the mother herself re-marries, in which case custody may be awarded to someone else such as the girl's grandmother or aunt. This is based on the Prophet's (SAW) words to the divorcee:
"Your right to custody of the child is greater as long as you do not remarry." (Ahmad, Abu Dawud, and Al-Hakim graded it Sahih)
Information from The Rights and Duties of Women in Islam
By Abdul Ghaffar Hasan