Have I sinned by prohibiting what God has made lawful, or by seeking forgiveness after advising a child to listen to music, assuming she is not yet accountable?

These are whisperings (waswas) that you should not pay attention to. Accustoming a child to comply with the rulings of Islamic law and to observe the limits set by Allah is required. The jurists have stipulated that the guardian of a minor should keep him away from forbidden things and command him to perform acts of worship, so that he may become accustomed to them. Therefore, the responsibility for preventing a minor from listening to musical instruments and the like falls upon his guardian. Seeking forgiveness (istighfar) is a good act and there is no sin in it.