Yuki's main motive is to shame the couple. In one of her entry, she wrote that in June she confronted ZR and told her that she would post the story if she and Alvin become a couple. By doing so, she has made it a point of no return for the relationship between she and Alvin. Even if Alvin has any conscience or regrets his acts one day, he'll remember how vengeful and manipulative Yuki is and would not return to her side. He could even feel glad now that he made the right choice by not marrying her.
By posting the story, Yuki gets to act as the victim, all will pity her. Maybe another man will come along to marry her off to save her from her pitiful state. I wonder what's her background, so influence and have so many friends to help her fan up the issue.
Nobody would want to end up in her state, we all know someone who has been betrayed by love. However, fanning up this case so big is not to Yuki's advantage as well.