As for motivation, I felt that she was simply taking what she felt she needed. Anja was going to leave her anyway, it didn't matter if she killed her. And killing her would allow her to have Loki. (She would probably eat her, also. And I'm not just saying that to be gross. I mean, it's the practical thing to do, especially being left on her own.) I think she wanted Loki, or at least the intimacy that she had with her first love, or to consummate what she never did with him, I'm not sure. And that she was crying because she was alone again. It might not make sense to cry after killing/running off everyone, but she would have been alone anyway, at least she would have this one thing first.

I'm not sure, though. Like you said, I wonder how the book reads.