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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we ask Allaah to relieve you of what you are experiencing. We recommend that you try to forget this painful memory, as there is no benefit in remembering it besides re-experiencing the pain and grief. Indeed, a wise believer should not grieve himself.
With regard to those who sexually abuse children, they fall under the threat of the general texts about injustice and the consequences of evil-doers. If their abuse reaches the degree of Zina, then they fall under the threat against fornicators and so on, but there is no special threat for them in the Quran or the Sunnah.
As regards his wife, the basic principle is that no bearer of burdens bears the burden of another person. So there is no relationship between the wife and the transgressions of her husband. Also, she is not obliged to believe the accusations against her husband; and even if she believed them, she is not obliged to separate from him according to the view of many scholars. What she should do is to give him advice and remind him of Allaah.
As for the causes of such abuse of children, there is no doubt that being heedless of and distant from Allaah and having an evil soul and a filthy heart are the major causes. There are also other causes, such as looking at forbidden things, and so forth.
Concerning the victim, she is like all other wronged people whom Allaah has promised to aid. If she incidentally remembers what happened to her and she is patient and seeks the reward of Allaah for that, then she gets the reward of those who are patient, based on the Hadeeth which reads: "Whoever is afflicted with a misfortune and remembers that misfortune and says 'inna lillaah wa inna ilayhi raaji‘oon (to Allaah we belong and to Him we shall return)', even if the misfortune happened a long time ago, then Allaah writes for him the same reward as when he is afflicted with it." [Ibn Maajah] Al-Boosayri said: "Its chain of narrators has some weakness."
If she forgives the one who abused her, then she gets the reward of those who forgive. Perhaps pardoning and forgiving the aggressor would help to forget the misfortune.
Finally, if an abuse or injustice happens to a person, then this does not mean at all that Allaah hates that person.
Allaah Knows best.