Is it permissible to wear the hijab in front of one's maternal aunt's husband, who is considered like a father figure and mentor, especially if the parents object and the fiancé insists?

The خال's (maternal aunt's) husband is a non-mahram (أجنبي). The daughter of his wife's sister is Haram for him to marry by way of جمع (simultaneous marriage to two sisters), not by way of أصالة (inherent prohibition). Therefore, she must interact with him as a non-mahram. It is not permissible for her to display her adornment to him, because he is not among those mentioned in the Ayah of An-Nur. Obedience to the husband in what is permissible is more emphasized than obedience to one's family. It is commendable to give a gift to the خال's husband or supplicate for him in return for his kindness.