The reason of the incidents that happened kinda makes sense for their age, but man… People really need to learn how to talk – For what I could get, she didn't really cheat on him, it was a very stupid jealous induced misunderstanding. Her friend Natusiki (Yep, that girl of the mixer is not hitting on him), said it was strange that he expends so much time with his friend and in the eyes of everyone, HE WAS CHEATING ON HER WITH AYAKA, and then she's starting acting cold and weird around him.
Until we see her point of view of things, it does seem like she's a total cheater… But, she actually seems to really like him... It's difficult to cheer for her tho, 'cuz we see her as a villain since the beginning and the other two are away more interesting at this point, but they did seem to be really cute together, until Reina started to being aware of Ayaka as someone more special to Yuta than herself, and basically that's why she didn't say anything when he asked to break up. Ah, the holding hand's thing, right… It was someone from a beauty pageant that would occur in the university, she declined the invite, but the guy kept insisting, and she didn't talk with Yuta, cuz they're in an odd situation at the time, being jealous and so on... So, instead of talking with Yuta, she decided to just cold shoulder him for a month or so to decide what to do, but some rumors started to appear that she would break up with him, that's why some people started talking about that in his club, and that pageant guy, started to hit on her, but she wanted to see if it was really possible to be only friends with someone of the opposite sex... Guess what? The guy started hitting on her, and he held her hand, she decided to try and see how would it feel to hold someone else hands instead of Yuta, and thinking if it was okay for he and Ayaka could go out (not dates, but people said that what's looked like), she kept thinking about Yuta, and shove the hand of the guy out, but that was away past the point that Yuta sees them in front of his house what she only noticed after shoving the guy hand away. In short... Prepare for a 3 girl story, cuz for what I got, she's not giving up, cuz she also could not stop thinking about him for the whole time, the posts she did, the hair color change and so on was trying to fill the void that breaking up left on her, well, until they met again. After some more thoughts after meeting him again and realizing that she's the 'bad wolf' of the story, she goes again talk with Natsuki, saying that she hates the moon, cuz it can't shine without the sun (basically saying that Yuta was as bright as the sun to her), and that she decided that neither Yuta (as people talked that he and Ayaka were cheating on Reina) nor she had cheated and that she couldn't give up on him.