Kinda hilarious in hindsight-ish, since regarding the current event in AL it showed that the two didn't get along when they were younger (not as young as the pic above portrayed).
And, way late on this, but to provide some context to their relationship. For most part, in the main storyline, AL's Akagi and Kaga's relationship is more or less kinda sister-like, with Kaga being somewhat subservient to Akagi. That said, during an event that was set before AL's story mode, their relationship is a lot more antagonistic, with Kaga even calling Akagi then a "bootlicker". Things that transpired during that event made Kaga take on a more sister-like role to Akagi. Houshou is more of a bit player during that time, being the one who eventually helps get used to being a carrier instead of a battleship and battlecruiser.
In the recent ongoing anime, Akagi and Kaga is still kinda like sisters... just more laced with yuri on Akagi's side.
