Is it permissible to abandon one's wife and neglect her marital rights due to discovering her infidelity, while continuing to fulfill the needs of the children?

If it is proven that the wife is speaking with foreign (non-mahram (definition)) men in a forbidden manner, she must be advised and prevented from doing so. It is legislated to abandon her (in bed) so that she may be deterred. If abandonment does not work, then it is not legislated. If he marries another, he must be just between his wives in spending the nights and other matters, otherwise, he will come on the Day of Judgment with his side leaning. Not giving the wife her rightful Islamic due is a grave evil and injustice. Therefore, it is obligatory to be just between the two wives, and to either fulfill her needs (chastity) or divorce her if she does not become upright.