Is divorcing her husband, who practices sodomy, the solution for her to reform his situation, especially since she has three children and fears for them and herself from diseases, after she has despaired of reforming him?

Sodomy is one of the gravest sins and obscenities, and its perpetrator deserves punishment and disgrace. If the husband commits this disobedience, he must be advised and warned of Allah's punishment, and helped to strengthen his connection with Allah, associate with the righteous, and attend gatherings of knowledge. If he persists in committing this grave sin, then it is better to seek a divorce from him.