It's definitely a positive sign that you are working on establishing your own healthful boundaries; it's not clear to me whether "the rage intensifies" is a reference to your own state or your daughter's - but either way I hope it's something that calms down and doesn't resurface with the same intensity in the future. The good news, in a world of bad news, is that the majority of BPD cases get substantially less uncontrollable as they exit the teen years and continue to age. They don't radically become entirely different people, but they also decrease the frequency of things like suicide attempts, often drastically reduced...so God-willing things will get better, just endure the hard times now.
It sounds so frustrating for her to have been misdiagnosed, as AskingWhy says - unfortunately it's not uncommon for general professionals to confuse BPD and Bipolar. Some doctors, nurses, even general psychiatrists and psychologists have made the mistake, and not as a slip of the tongue, but casually dismissing BPD as some lesser variation on Bipolar. The truth is, professionals are advised against taking Borderline patients among their clients; if a certain percentage (I believe the number quoted to me in a specific region was 8%) of their clients have BPD-symptoms then their insurance rates skyrocket...and they're told from the start, that unless they are specialists, they are not likely to be able to help BPDs. So you end up with a medical community that has "BPD specialists", "Others, who know what BPD is and stay away from it", "Others, who didn't pay attention to what BPD is because they intend to stay away from it" and "Others, who think they are qualified and experts for anything to do with mental health...but are wrong".
As it sounds like you've experienced, Bipolar meds like lithium really do nothing to help with BPD. Many people will say that CBT/DBT therapy works wonders (big hitch here is that with their self-image being dependent on others' perceptions of them - they can be notoriously difficult to get to complete a course), and others will say that meds have been literal life-savers. (There is no "prescribed medication for BPD", it's all just treating the symptoms - but anxiolytics like Ativan and Xanax are common, SSRIs sometimes, etc).
A parting question, and a thought -
Question: You mention the Bipolar was diagnosed, but haven't mentioned how it was determined she's BPD (other than I assume you recognise her actions); have you been able to get a professional to see her in regards to BPD? Does she accept that she has BPD or Bipolar or neither?
Thought: Since there are hereditary and childrearing causes for many BPD cases, it's common for both parents and outsiders to start questioning whether the parents did something 'wrong' and to question whether they possibly also have (much milder) BPD themselves. It sounds like your own mother might be believing that - which doesn't necessarily mean it's true because the one thing with which this forum will agree...BPDs are cunning experts at playing family alliances against each other for maximum destruction. Your mother may back your daughter for a year or more insisting she's an angel, before discovering randomly one morning that she has woken up to find herself demonised and cast as your daughter's arch-villain...and only then will she understand. I wish I had advice on how to explain BPD to those who haven't studied it, but as this post began...even general professionals can be obtuse about what it actually is.
If it gets confirmed as BPD - deal with specialists; because paramedics, police, therapists, lawyers, psychiatrists, well-meaning friends and relatives...those who dismiss BPD as "I think it's like Bipolar but y'know, slightly different", are going to ultimately be a huge liability for being detrimental to the situation.
