Yoshiki Kitazawa is really a manipulator . . .. . . and isn't the severe Cloud Cuckoo Lander that she makes herself out to be. Think about it. Most of her actions seem to be purposely geared towards affecting Eiri and Shuichi's relationship. It was her that helped Eiri say the right things to win Shuichi back. When Shuichi kissed Reiji due to his anger at Yuki, Yoshiki was the first to pop out of literally nowhere a smack him around. This lead to her agreeing to help them both by dressing up as his brother Yuki Kitazawa and forcing a confrontation with Eiri. After meeting Eiri for the first time in New York, and seeing how Eiri was still consumed by guilt over the death of Yoshiki's brother, which Yoshiki wholeheartedly agrees he deserved, she may have decided to try whatever she could to help Eiri overcome his past and try to prevent Shuichi and Eiri (especially Eiri) from screwing up their relationship like Yuki (her brother) screwed up his, and help the two grow closer. This would mean that Yoshiki knows exactly what she's doing, and her floaty personality simply makes it seem like she doesn't know what's going on. This is explored even further in the next WMG . . .
Eiri and Shuichi will end up adopting Riku Kitazawa as their son by the end of Gravitation Ex (if it ever finishes)And Yoshiki is planning for this to happen. In Gravitation Ex, after Eiri and Shuichi leave the cemetery in New York, Yoshiki says, "I'm doing a cruel thing, aren't I?" This hints that she knows the effects Riku is having on the couple, especially Eiri, but still plans on leaving him with them since she believes it will be what's best in the long run. It may be possible that this is when she called in the favors owed to her by Shuichi and Eiri. Perhaps she's hoping that this will help Shuichi and Eiri grow as a couple, and also act as the final step in helping Eiri completely move on from his past. Even if they don't adopt Riku, that doesn't mean that simply dealing with him for a week isn't meant to serve a greater purpose. A purpose that Yoshiki wanted to happen.