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.
There is a difference between the permissible mixing and the forbidden mixing; if men and women are in one room and there is no partition between them but they abide by the Islamic requirements, like women observing Hijab and not speaking in a soft and attractive voice to men, and so forth, then in this case, this is permissible and it is permissible for you supervise such mixed courses.
However, if the mixing is in a forbidden manner, like revealing the ‘Awrah (parts of the body that must be covered in Islam), not lowering the gaze and speaking in a soft and attractive manner and the like, then this is not permissible as we clarified in Fataawa 88227 and 83953. In this case, it is not permissible for you to supervise such mixed courses or help in organizing them; rather, you are obligated to refrain from this as there is no obedience to a creature in disobeying the Creator, and cooperating in sin is forbidden as Allaah Says (what means): {…but do not help one another in sin and transgression.}[Quran 5:2]
With regard to the ruling of advertising such mixed courses, it is the same ruling as supervising it and the details that we previously mentioned apply to it.
As regards entering upon the female director and dealing with her within the limits and requirements of Sharee’ah, like avoiding forbidden looking, touching and the like, then this is permissible and since her office does not have a door and its walls are transparent (made of glass), then your presence with her in the office is not considered a forbidden seclusion with her in the presence of other employees in their offices.
Concerning your work in this company, if your job is limited to lawful kinds of work, then it is permissible. Nevertheless, since work in this company includes what you mentioned and you are not able to forbid evil in it or reduce it, then in order to be on the safe side, it is better to quit working in that company and look for another job where there is less temptation and where there is no cooperation in sin. For more benefit on the pre-conditions for a woman to work, please refer to Fatwa 82399.
Allaah Knows best.