Is it permissible for a single man to marry a divorced woman who has repented from fornication and has children, if he wishes to care for them and marry her after verifying the sincerity of her repentance?

If a man is certain of a woman's repentance, there is no impediment to marrying her, because true repentance removes the descriptor of zina (fornication/adultery). Indeed, one who repents from a sin is like one who has no sin, and repentance erases sins. There is no impediment to marriage simply because she is older or a thayyib (previously married woman), even though the general principle is that it is preferable to marry a virgin. Nevertheless, marrying a thayyib is permissible and may even be preferable in some cases.