How can parents be persuaded to accept marriage to a divorced woman with children, and is it permissible to marry her without their knowledge or her father's knowledge, especially given that the young man has performed Istikhara, feels comfortable with this marriage, and is capable of taking on the responsibility?

A man marrying a woman older than him, or vice versa, is permissible in Islamic law as long as both parties are consenting. The Messenger of Allah, peace and blessings be upon him, married Khadijah, may Allah be pleased with her, and she was older than him, and A'ishah, may Allah be pleased with her, and she was younger than him. Umar ibn al-Khattab, may Allah be pleased with him, married the daughter of Ali, may Allah be pleased with him, and she was much younger than him. There is no harm in that.

If there is a benefit in marrying your paternal cousin's daughter, such as being kind to her children and raising them, then she should not be rejected simply because she was previously married or is older.

It is advisable to persuade your parents by mentioning examples from the Prophet's biography and seeking help from scholars to influence them. However, you must obey them if they insist on refusal.

It is not permissible to marry your paternal cousin's daughter without her father's permission, unless her father prevents her from marrying someone suitable for her. In that case, the guardianship transfers to the ruler or the judge.