Aki is definitely in love with Yori, and she's doing this to push Himari into a decision. I think she realizes that there's a very low chance of this working out in her favor (Himari has to give up which is unlikely and Yori has to fall for Aki which is unlikely), so she's -mostly- doing it to help Yori out of a rough situation for her. I don't think it's done purely or even mostly out of spite or anger (though there's probably a little of that in there - feelings are messy).
This manga's relationship gives me mixed feelings, too. It's good they're being honest with their feelings here, and this does mirror real-life relationships way closer than most manga. Himari's reaction is a common reaction you would expect from somebody who has been previously straight but is really into somebody as a close friend. The problem is that it is also essentially stringing somebody along when the end result may be not having a relationship at all, even though Himari isn't intending that (and does appear to be somewhat falling in love with Yori).