Is it permissible for the father to request custody of his two children if the mother is employed and does not have sufficient time to raise them, while the father is capable and can provide a good family life?

If the wife stipulates to her husband that she will continue working, he does not have the right to force her to quit, based on what was narrated by 'Uqbah ibn 'Amir, may Allah be pleased with him: "The conditions most worthy of fulfillment are those by which you legalize intimate relations." This applies if her work adheres to the Islamic guidelines.

However, if she did not stipulate this, she does not have the right to work outside the home except with her husband's consent, and he has the right to prevent her; because it is obligatory for her to obey him in what is good, as stated in the hadith (definition) of Abu Hurairah, may Allah be pleased with him: "No woman should fast a day from other than the month of Ramadan (definition) while her husband is present except with his permission," and his saying: "If I were to order anyone to prostrate to anyone, I would have ordered the woman to prostrate to her husband," and his saying when asked which women are best: "The one who pleases him when he looks at her, obeys him when he commands her, and does not contradict him concerning herself or her wealth in a way he dislikes."

If the husband is well-off, the wife should not work due to the resulting neglect of the home and children. The husband may take the children with him due to her preoccupation with them, and because he is their guardian. When the parents reside in different places, the father has more right to custody when traveling, because he is usually the one who disciplines his son, raises him, and preserves his lineage.