Should a wife remain with her husband or separate from him if she discovers his physical infidelity, and does the fatwa differ if the infidelity is on the part of the wife, and does Islam oppress women or empower them in such cases?

If the husband betrays his wife physically – such as by engaging in an illicit relationship with a foreign woman – and this is proven, then he has committed a great evil. If the husband does not repent, the wife has the right to seek separation; indeed, it is commendable for her to do so, due to his abandonment of the rights of Allah Almighty, and there is no difference in this regard between a man and a woman.