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.
If it is proven that your husband is actually having extramarital affairs and committing immoral acts with women, then he is in grave danger. We have underlined the prohibition of fornication and the punishment for the fornicator in this worldly life and the Hereafter and also the prohibition of having illegitimate affairs, so please refer to Fataawa 131407 and 87160.
The matter is not whether you forgive him for what he has done but is graver than that. Your husband must be advised and reminded about Allaah and the need to repent of his sin before death takes him while he is still sinning. The conditions for the validity of repentance are detailed in Fatwa 86527.
We have previously provided many guidelines regarding divorce; so please refer to Fataawa 131407 and 87160.
We wish here to emphasize the importance of supplication. Verily, the hearts of the sons of Aadam are in the Hands of Allaah; He turns them in any direction He wills.
You are not obliged to ask for divorce; however, if your husband does not repent of his sins, we advise you to leave him and request divorce even if in return for compensation. Living with such a man, given these circumstances, can consist of an affliction and incur harms on you; he may even be a bad influence on his son.
In case of divorce, the custody of your child is granted to you as long as you do not remarry. If you remarry, the custody is granted to your mother or the one who is most entitled to custody of the child after the mother. His father has no right to custody in this case since bad moral character is a legal impediment to receiving custody of children according to the most valid opinion of the jurists. For further information, please refer to Fataawa 84618 and 90461 about custody of children.
Allaah Knows best.