If I recall, she wants you to kill Nilsine to make her family feel bad for casting Muiri out onto the streets. She's mainly using Nilsine as an object of her revenge upon the parents. Edit: I should also add that Muiri believed that by killing Nilsine, the family would take back Muiri out of guilt, or something like that.
Alright, so she wants to kill an innocent person more or less. And also to marry her I need to join the Dark Brotherhood which I did not intend to.
A pity. She looked pretty, and we have in common alchemy interest.
I'm trying to find someone with personality and it could prove impossible task seeing how few options there are in the first place even when you ignore the race, and then few lines spoken by a NPC.