In the catholic perspective and about the link between him and his wife , his wife should try to forgive him under some conditions if and only if he is so sorry and if he has received the obsolution after a confession. In the marriage, forgiving is the principle, otherwise where is the charity between spouses.
In the catholic perspective and about the link between him and his children, if he is so sorry and if he has received the obsolution after a confession, in the case where his wife can not forgive, his wife, the mother of his children has no moral right to use the legal civil system by using his cheating in order to deprive him to his parental rights.