What is the legitimate, God-pleasing solution for marrying the aforementioned girl, taking into account the mother's refusal and the existence of an alternative whom the mother approves of?

Young people err by being lenient with forbidden relationships, which leads to their attachment and then parental disapproval. Marriage based on a prior relationship is often unsuccessful, whereas traditional marriage is often successful. The mother's refusal of the marriage complicates the issue, and marriage without parental approval may not be stable. It is better to strive to convince the mother to gain her consent. If that is not possible, it is preferable to forgo the chosen girl to avoid straining the relationship with the mother, as depriving her of joy after a long life is not religiously pleasing.