The relationship between two soeurs is not exactly meant to be romantic. The soeur ideal is probably close to the purified Classic Greek ideal of elder-youth interaction.
(begin longish historical rant....)
The elder offers counsel, training, protection and shares experience, while the youth follows his/her example and offers help, relief. Bodily and sexual gratification, in contrast to the common perception, was NOT required. (In fact, in Plato's books, it seems that celibacy and moderation in the expression of sexual desire was praised).
The elder/youth relationship was not restricted to males only. In the archaic period , especially in Sparta and the Aegean Islands (which kept intact many matriarchic traditions) women were expected to follow this pattern of relationships. Do I have to refer to Sappho, here? In fact, if we take into context some ancient historians and poets, she was rather the rule than the exception
(...end longish historical rant)
In fact, from my watching of the anime, it seems that the relationship between Youko and Sachiko is the pure soeur relationship as it was proper and intended to be: The elder sister acts as a mentor, adviser and confidante while the younger supports and helps her (and offers ego boost in the form of admiration
). I take it that their becoming soeurs was a thing well thought, well-discussed and even calculated, unburdened by excessive emotion. (I may be extremely wrong here, I haven't read "Answer") Youko and Sachiko may have liked each other as friends but I seriously doubt they were attracted to each other or were emotionally close, at least mutally.
(I think that Youko might have such a HUGE crush on Sei that it renders her incapable of falling for any other, but that's only speculation...
)
Enter Yumi. Youko has proven, time and again, that she is an excellent judge of people and she immediately sees that Yumi has the major hots for Sachiko. She also notices that Sachiko is also attracted to Yumi big time. It also seems that Yumi can reach Sachiko emotionally in a way Youko cannot do. It's a different sort of relationship, more romantic than classic - if you get what I mean.
Youko makes a mental note and steps aside to let this relationship grow. It would be good for her little sister to open up emotionally, and the easy going, well-meaning, sensitive Yumi seems perfect for the part. Youko graduates, certain that her petite soeur will have someone to support her.
This doesn't mean that Youko doesn't care for Sachiko. She cares an awful lot, but she knows her limitations and knows what support she can or cannot offer. So, when she learns that Yumi and Sachiko have drifted apart, she does the best she can do - brings Yumi back.
Sachiko has suffered a loss and is vulnerable. No logic or counsel could help (the things Youko was capable of). Sachiko needed some affection and someone that could reach her heart, and Yumi was the one that could offer these (not Touko, which is probably impacted too by said grandmother's death and doesn't seem to be the sensitive, supportive type).
Too long, sorry...