I honestly think that the author/mangaka should have woven more of Yami into the story leading up to something like this:
Hikari notices that her friend Yami is more moody/emotional, and tries to take her out to lift her spirits. She tries to get Yami to tell her what is troubling her, with Yami rebuffing her on several occassions. Let's say on the 3rd try, Hikari tries to ask what the matter is. That is when Yami states she is depressed and says that taking care of her mom has become very wearing on her. And that is when she can lightly touch on her family history, her guilt over her mom and the boy that she pushed away (no name given yet, as she know telling Hikari is a bad idea). You can have Yami storm off because of Hikari's pushiness of trying to considerate or you can have them bond over this. (anyone's call).
So when Hikari see's Yuu kissing Yami, she can put 2 and 2 together and realize the boy she was talking about was Yuu himself. You can then cut into the flashback to fill in the details of her backstory, but due to the details given prior, you don't have to make it so long.
There. You have Hikari pulling in a third party character to make them relevant to the plot due to her kind personality, you get puzzle pieces about said character, and then a reveal later to Hikari (and the audience) that Yuu is the boy Yami was talking about. (along with a more condensed flashback).