All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is an obligation on a woman in menstruation or who had sexual intercourse with her husband to wash her hair until the water reaches the scalp when performing Ghusl (a ritual bath). The Prophet described the method of how a woman should perform Ghusl as he said: "She should use water mixed with Sidr and cleanse herself. Then she should pour water over her head and rub it well till it reaches the roots of the hair, after which she should pour water over it." [Muslim]
Therefore, it is not permissible for a woman to avoid this when performing Ghusl except for a necessity. It does not appear that there is a necessity for your wife to avoid doing this obligation as it is possible to have sexual intercourse early in the first part of the night and perform Ghusl then, or to use a hair dryer and so forth.
It should be noted here that in principle a woman should remain in her own home, do the house work and nurture the children. Allaah Says (which means): {And abide in your houses …}[Quran 33:33]. So it is not permissible for a woman to go out of her home except for a necessity or a need that is religiously acceptable. If there is no necessity or need for your wife to go to work then she should leave this work. Rather, she is obliged to leave it if it entails transgressing some religious limits, like being in seclusion with marriageable men or mixing with them, or going out without Hijab, or being negligent about the rights of her husband and so forth.
For more details, please refer to Fatwa 82399.
Allaah Knows best.