^ There was never hate involved in their relationship, so that wouldn't be it. Their wargames are straightforward competitions between teams which didn't dislike each other, which is why Kaban's more sports-like "wargames" were received so well.
I think their date in episode 2(?) was pretty straightforward, really. Hotaru probably wants a romantic two-girl friendship and Komari would give her that. I hate to admit it, but Kurogane Ken probably read these characters accurately - all Hotaru would have to do is say girls in Tokyo have romances with other girls all the time and Komari's desire to be special would take over.
Jesus, this is just so cute. Eli so contented she doesn't even notice her strap's slipped, Umi too embarrassed being with her crush to feel anything else... Sweet girls. Protect them.