What is the ruling of Islamic law regarding the wife remaining married to the man after her affair has been exposed and it has become known that her children are not his?

If the wife repents sincerely and shows signs of righteousness, he should continue with her as if nothing happened, for "the one who repents from sin is like one who has no sin." If the children know, he should inform them that he kept her to cover her after her repentance. However, if she does not repent, he must divorce her to preserve his honor and the sanctity of his bed.