To me it doesn't feel like he accepted her apology, more like he just doesn't want to have anything to do with the matter anymore. I think now that he has Hestia he just wants to put the past behind him, but that doesn't mean he's forgiven her. For example, I know that personally. I used to be bullied and my bully never apologized. I don't hold a grudge against her though because I've come to terms with the past and it's no longer relevant. But that doesn't mean I've forgiven her, I just don't care, just like she does. She even asked me for advice about a job once, and even though she never apologized, she asked me years later and acted like it hadn't happened. But I think even if she had apologized and meant it, that wouldn't have changed my past, present or future, so it wouldn't have mattered to me either way, and I think Kael sees it the same way with Diana.
That’s why I have accepted in quotation marks
You people seem to be forgetting the main reason why she thinks she came back. It was to actually serve Kael and get the justice he deserved. She gave Diana so many chances to actually rectify herself and apologize to Kael because she thought it was what she was DESTINED to do. Now, Diana is playing with Kael’s feelings again ON TOP OF her doing everything she can to bring him justice (aka the reason why she thinks she came back so to hear that he “accepted” Diana’s half ass apology, that’s why she’s stressing because she can’t do what she thinks she was bought back to life for). She is trying to make things fair for her love who DIED by these people who didn’t show remorse in the past. Like.. yes Kael has moved on but look at the big picture from her stand point. I would be mad too because out of everything I have done for you, you’re going to accept an apology that wasn’t an apology???