Hi Cape to Wings and welcome to bpdfamily.
Your situation is unique in a lot of ways.
1) It's really unusual for your daughter to self-diagnose. I am sure she is in a lot of pain and is trying to figure out how to get control of her life. That is incredibly positive and encouraging!
2) As a parent, you are very supportive and compassionate. That is also really helpful.
BPD is a hard illness. The behaviors of your daughter that you love, possibly her creativity, passion, caring disappear and are replaced with rage, aggression and inability to communicate without being triggered. That's the double edged sword that people caring for or caring about someone with a mental illness face - the loss of behaviors you love and the addition of behaviors that challenge you. So, I really understand what a whirlwind it can be.
You mentioned your daughter is trying to regulate her behaviors/reactions. Is she receiving any therapy or in a program like DBT? If not, I really recommend encouraging her and assisting her in finding a therapist and group for DBT. It's the most effective, current treatment for BPD.
Second, you mentioned that her child's father is in the volatility and possibly in domestic violence. That cannot continue. There are links on the website here to domestic violence tools,
https://bpdfamily.com/discussions/search-info4.htm. Please send these to him and tell him about this website. Sounds like he needs support.
Third, is your grandson seeing a child therapist? If not, is it something that you think you could suggest to your daughter? At his age, the therapist should be entirely play based and also familiar with working with children with BPD parents. On your and your husband's side - yes! please keep giving the parents breaks when and where you can, as it also gives your grandson access to healthy, safe, consistent attachment, which he desperately needs. When you are with him, provide him with a lot of validation ... .validation to whatever feeling or experience he shares. Ask validating questions that can help him sort out his feelings, maybe through stories or television shows, like ":)oes it feel safe when people are yelling?" This type of question gives a kid a chance to speak safely and be heard. He will need as much of that you can give him.
Lastly, there may be a board that is a little better suited to this topic. Would you be okay if this thread were moved to either the parenting a BPD board or the co parenting a child board?
I really appreciate you coming here to ask questions and learn. Your daughter has a good ally. And it is incredibly stressful and hard to negotiate the ups and downs of BPD. There is a lot of great information and resources and community support on this website, and I hope you keep reading and posting.