How do I deal with my wife who has started to commit to religious observance but still refuses to wear the niqab, does not care about correcting her recitation of the Qur’an, and is lenient regarding the rulings of menstruation, while it is difficult to guide her?

Your wife is persisting in a grave error, especially concerning the issue of prayer, the abandonment of which is feared to lead to apostasy. You have fulfilled your duty in guiding her, and the appearance of fruit from that, even if incomplete, is a positive step. Continue with advice and guidance, for "it is better for you that Allah guide one man through you than for you to have red camels." Remind her of Allah and teach her the status and rulings of prayer. Try to help her read the Quran correctly, as an error in Al-Fatihah that changes its meaning invalidates the prayer. Be patient, and make her love learning her religion by encouraging and being gentle with her. Make abundant supplication for her guidance.