In my humble opinion, I would say that you shouldn't go report her.
I suspect that if this woman is taking these actions, then she's lashing out at others because she is hurting herself. I also suspect that she'll have many chances to learn the lesson of "What goes around, comes around". I bet she's hurting herself much worse than you could ever hurt her.
However, the issue is not about what this other woman is up to...but rather bringing you and husband closer together.
He is opening up and sharing with you. It would be hurtful to reward that with behaviour that he sees as a form of betrayal.
It doesn't matter that it isn't a betrayal...perception is everything.
I think you are doing a great job of piecing...keep up the good work.