What are the waters of man and the waters of woman, and when is the newborn a male or a female, and is there a Hadith from the Messenger of Allah, may Allah’s prayers and peace be upon him, about how to know the sex of the fetus?

The oath you took with your wife, that she would not visit a specific family, is considered based on your intention and the reason that made you swear. If there was a reason for the oath and it has ceased to exist, then you do not break your oath if your wife visits the family. However, if you conditioned her divorce upon that visit occurring, without considering the reason, then her divorce takes place if the sworn-upon act occurs.

As for the man's fluid, it is white and thick, and the woman's fluid is yellow and thin. The child will be male if the man's fluid overrides the woman's fluid, and female if the woman's fluid overrides the man's fluid, as stated in the Hadith of Thawban.