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.
First of all, you should know that it is not permissible to accuse the husband, or any other person, of committing Zina (adultery) without clear evidence. If a woman is certain that her husband has committed adultery – we seek refuge in Allaah from that – then she must forbid him from doing so, frighten him of Allaah, and urge him to sincerely repent. If he repents, then she should have good marital relations with him and pardon him for his past sins, as repentance wipes out previous sins and a person who repents from sin is like someone who has never committed that sin. For more benefit, please refer to fataawa 170305 and 120656.
If the husband does not repent and insists on committing adultery, then she has the right to take the matter to an Islamic court or an authority that can act instead, such as Islamic Centers in countries where there is no Islamic court. It is the court that can decide whether or not seeking divorce has sound reasons, and if there are sound reasons, whether or not it will be with compensation (keeping the bridal gift or giving it back to him).
Allaah knows best.