What should I do if I have advised my wife gently to stop listening to music, and she is convinced that it is permissible as long as her words are permissible, and she listens to it while doing household chores, and if I command her to stop, she will do so without conviction because there is nothing to entertain her in the husband's absence?

Allah has granted the husband the right of guardianship (qawamah) over his wife, and this includes encouraging her to perform religious obligations and avoid prohibitions. If the music the wife listens to is permissible, then there is no harm. However, if it is forbidden, then it is obligatory to prevent her from it and to educate her about its Islamic ruling. It is also important to cooperate with her in acts of obedience and in reciting the Quran. Permissible anasheed (Islamic songs) can be offered as an alternative to forbidden music.