I found over the years that the best approach was to state once that I could not speak for N/BPDx, only myself and that I was open to feedback and ideas about how to correct behavior. Then let it go.
I did ask for separate parent-teacher interviews, and anytime there was an IEP/504 meeting, asked that the school try to hold them separately. One time they held it with both parents attending and N/BPDx was so hostile toward me that they went back to separate meetings.
When you are given advice that is offensive (i.e., both parents need to be on the same page) one response is, "I couldn't agree more. Do you have solutions that have worked with other divorced parents who don't see eye-to-eye about violence toward others?"
Inside, you can just roll your eyes and say "duh."
When people have simple solutions to complicated problems, sometimes it helps to ask them what they would do. It shows that you are open to improving your own skills, and makes them realize it's not so easy. After our divorce, S9 was supposed to take medication. N/BPDx didn't comply, and the child psychiatrist kept telling me it was important that S9 took the medication at both homes. I said, "I couldn't agree more. Perhaps this will be more effective if this comes from you, rather than from me, under the circumstances."
I believe her email to N/BPDx was met with a 10 paragraph response about how no one tells him how to parent his child.
My son drove a sharp pencil into the chest of another kid -- fortunately it was winter and the kid was wearing a padded vest. N/BPDx told S9, "Atta boy, he probably had it coming." I met with the school's family specialist and asked lots of questions. We invited S9 to the office and together we talked to him. Then, she suggested S9 wait outside. I asked her if she felt there was anything different I should've said or did.
Things like that can tell the school that you are working hard alongside them, rather than against them.
My concern about the actual behavior is that she has genetics that predispose her to intense emotions (this is true with my son, too). If so, you may want to get ahead of this by reading highly intense child books, or explosive child, and learn the skills recommended there. The biology of intense emotional kids means it is harder to regulate feelings, so behavioral outbursts are more likely, followed by the shame and maladaptive coping mechanisms that they see in their BPD parent.
You are intuitive and wise to be concerned, and she is lucky to have you looking out for her and paying attention to problem behaviors that under normal circumstances could be easily corrected, but with a BPD parent, can take on a life of their own.
