Maybe you are freaking the fuck out because you sense an actual threat to your marriage? From your description (which I realize is entirely from your viewpoint), she appears to be a classic cowgirl (someone who gets involved in a poly relationship for the purpose of splitting off one of the other partners into a mono relationship with said cowgirl/boy).
It seems wise to me when you put the kibosh on your husband's sexual/romantic relationship with her. Did you explicitly tell him it wasn't solely because of her instability and drama but because she wanted him for herself and was thus threatening the marriage? That she doesn't respect his marriage or his spouse? Does he understand that? It wasn't clear in your posts, at least to me. If you haven't had that explicit conversation about this with your husband - do it now.
You don't appear to be against the idea of your husband having other partners, or yourself having other partners (I've interpreted your 'polymono relationship' comment as you do not currently have another partner - not necessarily that you don't want one and are so mono - but I could have misunderstood this). You do appear to be against partners who want to at a minimum, induce drama, cause you to doubt your husband, make your husband ride to the rescue over and over, and possibly end your marriage. This seems like a very reasonable restriction. Lots of poly folk have some version of 'Don't date crazy' in their explicit or implicit guidelines.
That said, people can change. But generally not very fast. I too would be profoundly skeptical of 'I'm hurting!', 'But I've changed and everything is ok!' Usually change like that - resolving major behavioral and emotional triggers - takes a while and doesn't happen quickly while one is unstable, emotionally or otherwise. There are exceptions of course but it's been my experience that this holds true. If Ms. Cowgirl can walk the walk - maybe be friends only with your husband, show some real respect for you and your marriage, not put her needs and emotions first all the time - then maybe you can reconsider. But, if I was in your shoes, I would have to see some real concrete, long term actions on her part before I would consider any changes in my stance towards her and a sexual/romantic relationship with hubby.
Can your husband truly be only a supportive friend to her? I also would be skeptical here - mainly because he slept with her before talking to you about that possibility, even when he knew that you would likely be open to a poly relationship. He also sounds like a white knight, rescuer type of person. Which is great generally but white knights are often easily manipulated by real or imagined emotional or other vulnerability. Yes, she is in a difficult situation. Everyone would like support in such a situation - it's no fun being alone with few friends. But your husband didn't cause that situation, your and his relationship with her didn't cause her loneliness or lack of friends, and ending the relationship didn't cause her emotional instability. (Perhaps she lacks friends because she is a toxic personality? Given, this is a reach with the very limited information available but perhaps it should be considered.)
If he can be just friends with her, then perhaps cautiously support that. But if he doesn't see the cowgirl thing going on here, or sees it but discounts it, or is too into NRE/White Knight mode to care, then just friends may not be possible for him and for your marriage to survive.