How can I feel bad for her if she never even tried to fix them properly in the first place?
It's a bit more complicated that you make it sound like.It's not your classic misunderstanding situation, we talk about cheating with straight up lies. It's easy to say that Kaoru should walk up to Reiichi and ask him about that but in reality it's more complicated, Kaoru is in a mess after the whole Uta storm and she still trying to stay focus. Reiichi is now the only thing that keep her not alone, so it's difficult for her to ask Reiichi about that because if he say it's true and decide to go with Risako then Kaoru will be alone and depressed.
Honestly, yes Kaoru can do it but it's really difficult for herself right now to not but even salt in the injury and we talk about a simple cut here.