Is what I am facing in terms of marital problems due to violating the Istikhara, and what should I do given that I have children with her and do not want to wrong her by divorce?

There is no necessary connection between the existence of marital problems and seeking guidance (istikharah), nor should a wife be divorced because of them. Marital life is often not free from problems, and their treatment involves patience, utilizing legitimate means of reform, overlooking mistakes, and balancing good and bad aspects. Allah Almighty says: "And live with them honorably. If you dislike them, it may be that you dislike a thing and Allah brings through it much good" (Quran 4:19). The Prophet, peace and blessings be upon him, said: "No believing man should hate a believing woman. If he dislikes one of her characteristics, he will be pleased with another." The one who performs istikharah should proceed with the matter for which he sought guidance, unless Allah diverts him from it.