Praise be to Allah.
Working in mixed environments is not free of the risk of some haraam things happening, such as looking, being alone with a person of the opposite sex, or feeling attracted. Hence the scholars have issued fatwas stating that it is haraam, based on what usually happens. It says in Fataawa al-Lajnah al-Daa’imah (12/156):
Mixing of men and women in schools and elsewhere is a great evil and has serious implications for people’s religious and worldly interests. It is not permissible for a woman to study or work in a place where men and women mix, and it is not permissible for her guardian to allow her to do that.
Based on that, the father has no right to force his daughter to work in a mixed workplace. If he forces her to do that then she does not have to obey him, because the Prophet (peace and blessings of Allaah be upon him) said: “There is no obedience in sinful matters, rather obedience is only (required) in that which is good and proper.” Narrated by al-Bukhaari, 7257; Muslim, 1840.
This daughter must explain to her father the dangers of working in a mixed environment, and that it is haraam. She should remind him of his duty to protect his family and save them from the Fire, and she should do so in a wise manner and with beautiful preaching.
And Allaah knows best.