What is the intended meaning of Ibn al-Jawzi’s text that prohibits insistence in supplication if one’s prayer is not answered, and how can this be reconciled with the urgent need of the questioner to supplicate that her family’s hearts soften to allow her to visit the family of her deceased fiancé?

Firstly, if the marriage contract was concluded, then the husband's father becomes a mahram (definition) to you, and you must observe the iddat al-wafah (waiting period after death), which prevents you from going out. However, if the contract was not concluded, then he is a stranger to you, and his father is also a stranger. In this case, you are not required to observe any iddah (definition) or ihdad (mourning) for more than three days.

Secondly, there is no such thing as a superficial dua (supplication). The Messenger of Allah, peace and blessings be upon him, commanded us to ask Allah for everything, whether great or small. Your need to visit the family of your deceased fiancé to provide comfort for yourself and his mother is a noble need that deserves dua and persistence, even in obligatory and supererogatory prayers.

Thirdly, persistence in dua is among the good deeds of a servant. The statement by Ibn al-Jawzi, which might suggest not being persistent in a request after it has not been answered, should be understood in relation to several matters: that the persistence might be concerned with achieving the request without fulfilling the status of servitude, or that the persistence occurs after the desired outcome has passed, or that the persistence is for trivial worldly matters while neglecting religious affairs.