Call me jaded by reality, but I don't think you understand what a performance improvement plan is. Its a way for an organization to generate documentation to terminate an employee.
Eh, I had to put someone on a PIP years ago, and he did improve just enough to be taken off. It was frustrating because it felt like he
didn't get it, but at the same time, the performance issues we raised were corrected, and his work was just good enough, so I let it go.
The problem is that usually by the time you're at a PIP, the problems are big enough and entrenched enough that changing them is really hard. Any easy performance corrections have already been taken, and you're at the stage where the issues are down to fundamentals that are hard to shift.
Definitely check out the Ask a Manager blog - she address this kind of thing frequently. I think what she would advise would be to think about the results of the crappy behavior, like: employee is nasty and gives people the silent treatment, so they can't get their work done. So, you need her to respond within a day with the information requested (and correct and complete!), or with a notification of when she will be able to get that information to the requestor. And she needs to meet her deadlines.
You mentioned her being nasty to people who are holding her accountable. I'd recommending being completely explicit about what the expectations are that she's going to be held accountable to. Get as nit-picky detail-y as you need to. Have them in writing. Ask her to review these expectations (give her a day or so) and come back to you to confirm that they sound reasonable, or propose adjustments. Once she agrees to them, write them out and have you both sign them. Make copies, each take one. If she doesn't meet these expectations, that's part of her PIP reviews. Bring stuff up as soon as you find out about it.
It's a lot of work for you, and that's not fair, but it could also crystallize for her that maybe this isn't the right job for her. If you're explicit about expectations, and she can't or won't do it, this will make it abundantly clear to her that she needs to move on, since you're not going to change your expectations and just let her keep going as she's going.
One of the things that AAM is good for is helping managers view things a different way when they're frustrated with their people. Maybe she's angry because her responsibilities have changed over the years into things she's not comfortable with and hasn't had a say in (and hasn't been properly trained on). Maybe her responsibilities have kept growing and growing and she's worried about them growing into something completely unreasonable, so she's pushing back now as a maladaptive prevention technique. Or maybe she's just lazy and is hoping if she's difficult enough you'll all give up and let her go back to surfing the internet all day.