Doesn't matter much whether there is a diagnosis or not. Two things... .
1. Her: If she could lessen the Denial, Blaming and Blame Shifting then she could make real progress in long term therapy if she would apply the professional guidance in her life and thinking. However, she is an adult, you can't make her seek help, no one can, except her. (Generally it is not advised to mention BPD to the person, the 'label' can trigger overreactions and intense pushback.)
2. Son: He might be able to manage the relationship better if you help him learn what you and he are dealing with. With improved skills and techniques - see the workshops here - the confrontations may be less frequent and less triggering to her. A major part of living in close proximity to a pwBPD is learning how to set and maintain firm boundaries of behavior. While you and he may not be able to change her, you two can change how you handle contact with her. That's what boundaries are all about. Appeasing and compliance don't work, at least not for long. Firm and practical boundaries - based on what works and on overall insight and awareness - work best.
Thank you for suggestion. I started to explain to my son what BPD is. Thanks