Must I allow my wife to join a Quran memorization institute, despite my inability to drive her, the presence of a male driver on the institute's bus, and the availability of online learning?

A wife's keenness to memorize the Qur'an is praiseworthy and should be encouraged. It does not require her to leave the house; rather, she can learn through modern means or with one of the proficient female reciters. This is better, as a woman is commanded to remain in her home. Memorizing the Qur'an is not obligatory except for Al-Fatiha, and anything beyond that is Fard Kifaya (a collective obligation). Teaching one's wife the Qur'an is desirable if the legitimate Islamic guidelines are met and no harm results. The husband will receive a great reward if he assists her in this.