Upon rereading, I'm kind of impressed with the writing. There's not really much exposition outside of our MC's internal monologue, all of the plot points are coming across.
Anw, seeing how the sister took care of MC in place of their parents, still reached out and care for MC after she left home, plus having a good relationship with her ex-lover, I'd say that the sister seems like a really good person, not selfish or insensitive at all.
While the details might not've been all there, I think springing to any conclusions - on either side about her sister is pretty careless. However, I'm personally leaning towards "insensitive," but not selfish. She's done what's best for her, and that's all anyone should be expected to do (usually).
Kiku is thus far a sensitive person - she's completely tuned into Sena. She knows the crumpled paper is a letter. She knows Sena won't take care of herself if she doesn't come around. She knows that Yuuna is incredibly important to Sena. She grabs the phone away immediately when she sees Sena showing beginning signs of distress, and then proceeds to offer her physical comfort. She's pushy because she's so sensitive to Sena's needs.
Meanwhile, Yuuna sprang the fact she had a girlfriend on her baby sister out of (seemingly) nowhere. She flew off to another country for a work opportunity out of (seemingly) nowhere. After leaving, she chose to place the onus of reaching out on that same sister, leaving her alone with a convenient excuse. Then, at the most inopportune time for said sister, she chose to push the issue, and again sprang unpleasant news on her out of (seemingly) nowhere.
Now, maybe Sena is just really self-absorbed and/or a completely clueless fool, or maybe they're actually totally estranged and she's an unreliable narrator. Assuming none of those are true, all signs currently point to Yuuna being completely disinterested in someone who appears to be excessively dependent on her. Of course, all of this is completely subject to interpretation for now, as anyone could fill a dozen charitable explanations out pretty quickly. We'll see where it goes.