What is the Islamic legal ruling for dealing with a wife who admitted to fornication before marriage and corresponded with and spoke to a non-mahram man after marriage, given the doubt about the sincerity of her repentance?

It is not possible to definitively determine what is best for you, whether to stay with your wife or separate from her. However, if your wife repents sincerely, completely severs her relationship with that young man, and her condition improves for the better, and her past disobedience does not negatively affect you, then the advice is to keep her to preserve her repentance and for the sake of your children, especially since there was some negligence on your part towards her. But if you do not see sincere repentance from her, or if you are not prepared to turn over a new leaf, then divorcing her would be better for both of you. Choosing to keep her and conceal her secret is greatly rewarded, based on the hadith: "Whoever conceals [the fault of] a Muslim, Allah will conceal his [fault] in this world and the Hereafter." It is not a sign of effeminacy to keep her after her sincere repentance.