What is the legal ruling regarding divorcing a cheating wife and depriving her of the gold given to her as a dowry, while giving her another sum of money?

If a wife corresponds with a foreign (non-mahram) young man, she has committed a reprehensible act and disobeyed her Lord. The righteous wife guards her husband in his absence, as Allah Almighty said: "So righteous women are devoutly obedient, guarding in [the husband's] absence what Allah would have them guard."

The husband is advised not to rush into separation, but rather to counsel her and call her to repentance. If she repents and becomes upright, then he should keep her and treat her well to preserve the family.

However, if she does not repent, then separating from her is better, and divorcing her is recommended, especially if she neglects her obligatory duties to Allah or is not chaste.

The husband is not permitted to deprive her of any part of her dower. As for gold, if it was part of the dower or she owned it through a gift, he is not permitted to take it from her. However, if it was a loan from her for her to adorn herself for him, then he has the right to take it or leave it for her.