Apparently, only Shinka can see the love blossoming between Yuuta ad Rikka, further implying that she herself has no interest in him. Isshiki is totally focused on Kumin, though it'll take considerable effort on his part to make her fall for him, if that's even possible. And maybe Shinka herself wants some action as well, and likes him more than she's letting on (making it a possibility that she wrote him that love letter). of course, whrther she'd actually like him for who he is, or merely use him as a tool to keep up her 'good girl' reputation is up for debate.
So, the death of her father, and her mother abandoning her and her sister is why Rikka acts the way she does. That was quite a heart-wrenching revelation there. I still wonder why Touka didn't want her to visit her old (now gone) house. If she wants her sister to accept reality, why is so fervent on keeping it from her, knowing that it fuels her escapism?
I liked how we got some glimpses of Rikka's true self throughout the episode, especially later on.