Whoa, lots to unpack here.
First off, I am so sorry Haley was so desperate. But thank heaven she survived it.
I would consider Anna's actions to be comparable to if she'd aimed a loaded gun at your daughter and pulled the trigger. By all means, write her off.
But through all of this, although she's annoying, Jenny is innocent. How old is she? If she's a middle teenager (maybe 15 and up), then she should be past most meltdowns and will get over it. Sorry if that sounds harsh. But I would see if there's a way to leave the door open, even just a little bit. Again, Anna's behavior isn't Jenny's fault or responsibility. When Jenny matures, she will (we can hope) be far less annoying. And maybe there can be a limited relationship with her.
If she's younger than that, then excluding her, I feel, is more problematic. An immature child cannot be expected to be non-annoying 24/7. To condemn her for the twin sins of being too young to handle herself and unable to prevent Anna from bullying is truly unfair.
I mean, I'm not responsible for what my brother does, and he's not responsible for what I do. And we're both past our 58th year.
But let's get back to Jenny. In a large party, there should be fewer opportunities for one on one with her. You've got drinks to refill. Your kids have their cousins (or whoever you invite) to hang out with. I'm not saying to 100% ignore Jenny, but you have legitimate reasons for not paying perfect attention to her all the time.
So that's one way to maybe go. Here's another.
Since the mother has been good about this, is it possible to sit down—you, your wife, Jenny, and Jenny's mom, and talk a bit about it? Maybe Jenny will understand if you tell her something like, "Look, this has been a horrible experience for us and we need to protect Haley. Your being here, unfair as it may sound, will just remind us all about it. We would greatly appreciate you giving us some space right now. If you want to stay in touch, then we feel Haley would be really pleased if you sent her a letter or a card. It can be short. Just something to say you're thinking about her. Thank you so much for understanding."
Do you see what I'm doing here with language? I'm acknowledging it's unfair but at the same time providing a reason. And also demonstrating that things may not be like this forever, plus a way to extend a lifeline. And, finally, ending with a presumed understanding.
Anyway, those are my thoughts. And as for Anna, I do hope her mother is getting her the help she clearly needs. This is obviously not normal behavior. An intervention with a mental health professional might help keep Anna out of jail. Because this sort of behavior is pointing in that direction.
Again, I am sorry for what's happened, and I hope life is better for Haley, and you, soon.