I don’t fully know the situation, not even close, so if what I’m saying is way off you can just disregard it.
It sounds like you’re in a deadlock: You want to forgive her, but she won’t listen to you. She wants you to apologize for something, you think there is nothing to apologize for.
It’s a deadlock – both of you think you are right, and there’s no way either one of you will get anywhere if each one pushes her own agenda. The only way to get anywhere is if one of you gives in (me’vater) at least a little.
That leaves you, Sparkly, with two options.
Your first option is to keep pushing her until she gives in. This rarely works, and based on what you’ve said so far about the situation, I find this very unlikely to work.
Your second option is to give in a little yourself. Hear her out. Figure out why she wants you to apologize. Admit that you might be wrong, even if you don’t think so deep down. Once you step back a bit and loosen up the deadlock, you are more likely to get somewhere.