Welcome and hello

I'm glad you found the site and sorry for the pain and suffering that brings you here.
Parenting a child with BPD can be, like you said, filled with heartache. Many of the behaviors and other mental illnesses you mention are common to people with BPD, which means families experience them alongside their loved ones. I have read that the emotional burden for BPD caregivers is among the highest of all other mental illnesses, including schizophrenia.
There are skills that can be learned -- many of them are not intuitive, and require a lot of practice and patience.
How is your granddaughter doing? I imagine she must be affected by her mom's behaviors too.
What is one of the aggravating behaviors you are dealing with at the moment? Maybe we can walk with you and share things that have worked.
In the meantime, hugs to you for what you're dealing with on a daily basis. It's so hard, and our hearts can truly feel like they're breaking. Have you searched to see if there is a NAMI support group near you? Or maybe a NEA-BPD Family Connections group in your area? I tried to find one two years ago and recently they reached out, much to my surprise, since so much time had passed. From that group, I have discovered many other resources in my area, including DBT skills for families and a support group that meets once weekly. Hopefully there will be something like that close to you. And if you aren't able to find something right away, there are wonderful people here who know what you're going through.
You are not alone.
LnL