Hi Lennox58,
Welcome to the parenting board, and glad you reached out. It really is hard when our kids are depressed or struggle with any kind of mental illness. Does your daughter have self-loathing as well as hating the world? It's hard for me to see my son feel so down and hard on himself despite all the positive qualities he has.
Is your daughter seeing a therapist or taking any medication? Do you feel the BPD diagnosis helps you understand your daughter and her behaviors?
I do think it gets better. It's a slow process, not least because change is difficult. My son is doing better in part because I made a commitment to focus on turning the ship around, learning how to communicate with him and understand what had to happen in order for our relationship to improve. Expecting him to change without meeting him halfway would not work in our situation, he needed a buddy.

How are you doing? Are you taking care of yourself? It's easy to get swamped by difficult feelings when our kids are struggling to the degree they do. I never realized how hard it actually was to take care of myself until it become a necessity.
Let us know how you're doing, and make yourself at home here. Posting and share really does help and can make a big difference so you don't feel so alone. Plus the skills and tools here really do make things better.
LnL