Have I erred in reforming a forum that contains sections for singing, women's pictures, and other topics, after I stipulated to its owner that he repent and close only the fashion and song sections, while other sections remained that contain talk of love, flirtation, and audacious jesting?

What you mentioned regarding the errors in the forum is considered clear assistance in sin and transgression, due to the Almighty's saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." However, your missionary motive and your condition for your relative's repentance might make you excusable. You must repent to Allah and continue inviting your relative to repent. For after what has happened, you can do nothing but repent.