Is it permissible for me to continue a relationship with a young man, despite his mother’s rejection of me and her desire for him to marry her niece, and will Allah accept my supplication that He soften his mother’s heart and bring us together in a halal manner, knowing that my family is aware of this relationship?

If the relationship means meeting, talking, being alone together, and exchanging words of love, then this is not permissible Islamically. However, if the relationship means an Islamic engagement (khitbah) while avoiding what is forbidden, then there is no harm in it, and there is no harm in supplicating for the marriage to him to be facilitated. And this man should obey his mother if he does not succeed in convincing her.