Is it permissible, in Islamic law, for a wife to ask her husband, who works as a barber and owns his own business, and does not even take Fridays off, to dedicate an entire day to her and their two-month-old daughter, knowing that he finishes his work late at night? And what is the religious ruling if he refuses?

The default for a woman's work is to be in her home, raising her children and caring for her husband, to provide tranquility, stability, affection, and mercy. A woman should not work outside the home except out of necessity and with certain conditions, including: the work being suitable for her nature, adherence to Islamic law, proper covering (ستر), and avoiding impermissible seclusion (خلوة) and mixing (اختلاط).

If you are not in need of work and your husband is fulfilling his responsibilities, then your staying in your home and caring for your family is better and more important. It is your right that your husband designates a day for you to attend to your needs and maintain kinship ties, as long as no harm results from it. Marital life is built upon understanding, affection, and mercy.