Is it permissible to marry a divorced woman who has children, given the parents' disapproval and the fear of society's view, and of dealing with her children and ex-husband?

There is no fault in a man marrying a woman who is older than him or who was previously married (a thayyib). Indeed, the Prophet, peace and blessings be upon him, married Khadijah, may Allah be pleased with her, and she was older than him and a thayyib. However, one should not disobey a parent regarding marrying her, unless the man fears for himself fitna (temptation) or hardship.

As for the children, if there is a guardian who claims their custody, then custody belongs to him, as the mother's right to custody falls away upon her marriage. If there is no guardian or if he refuses, then the mother is obligated to care for her children. The husband has the right not to accept them before consummating the marriage with his wife, but he does not have this right afterwards.