Is the woman asking for divorce, relying on God, or will she, by making this request, have wronged her children?

We advise you to strive diligently to reform your husband and help him repent from evil deeds, especially abandoning prayer. If he repents and treats you kindly, then live with him and forgive him. However, if he remains in his state, then it is better for you and your children to separate from him. For divorce may be better: "But if they separate, Allah will enrich each of them from His abundance." He is also responsible for the maintenance of his children. Rely upon Allah, for "And whoever fears Allah - He will make for him a way out" and "And whoever relies upon Allah - then He is sufficient for him." Beware of suicide, for it is a heinous crime.