Thank you in advance for your advice! I appreciate hearing from you. 
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My mother has BPD and I have only just learned this. (I am 23 now.) She does not know she has BPD, and I have not tried to tell her she has this. I found out when I talked about my mother with a psychiatrist, and the psychiatrist explain that she may have BPD. I researched BPD, and realized that she does in fact display all of the symptoms. 

My mother's doctor has tried to diagnose her with bipolar disorder before, but I believe that is a misdiagnoses. My mother also refused to believe she was bipolar. My mother had a traumatic childhood, and there is no history of bipolar disorder in our family. Additionally, she clearly displays a manipulative characteristic which many people with BPD have. She has gone to therapy before, but I believe she did not have good doctors that could handle her properly. We are trying to get her into therapy again. Once we do I will be reaching out to the doctor privately to explain the situation, and making sure they are a good fit to handle her. 
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Currently I am looking for ways that my family can properly handle her, and help her. 
Specific situations I would like to handle:

1.) YELLING &amp; BELITTLEMENT 

When she yells and becomes irrational, her perception of things become very skewed. In these moods you cannot really talk to her. She seems to not remember things correctly, and rewrites history so that she is always the victim and everyone else the bad guy. This is when she will also state how she is worthless, and that everyone else (or you) are the worst. She will also threaten to kill herself, but has never made any attempts. I understand this is her way of reaching out trying to get us to prove that we love her all the time.

I have found that trying to calmly rationalize things with her does not work, and that she will continue ranting for 30+ minutes. Sometimes I will leave or hang-up to leave the situation, and she will later say sorry once she is calm. However, I am not sure if this is helping her.

2.) VIOLENT OUTBREAKS

She will sometimes break things while she is yelling. She does not do this with me, but she will do this to my father to rile him up. However, he never fights back. She wants a reaction and he does not provide one. So, she escalates to breaking things to attempt to get a reaction.

Currently my father will allow her to do what she needs to do, and clean up the mess. He will take the verbal abuse, and has since become numb to her yelling at him. I have recently suggested that he say something along the lines of "Whatever you need to do to get your feelings out I'm okay with. I love you and will still be here." Then to leave the situation in order to not take the verbal abuse, and wait till she is out of her irrationally angry mood.

3.) ABANDONMENT ISSUES &amp; AFFAIRS

My mother has cheated on my father for years, and they have been divorced for many years but are kind of together now. She abuses relationships/sex to feel she has worth and that people love her. I have seen her jump from relationship to relationship, making sure to have someone lined up. She has not been single since she was a teenager. She has always cheated on whoever she is with. Her relationships are often verbally abusive, but not generally physically abusive save one or two instances. 

Now that my parents are together she also assumes that my father is always going to abandon her, but he wants to make it work. She is the one that will leave for days at a time to be with another boyfriend. This is by no means a functional relationship, but my father loves my mother when she is more "lucid" and wants to be with her. He is not sure how to handle this, but keeps taking her back. If she refuses seek help later on, I have said that he will need to cut ties. 

Additionally, she will assume that me and my brother will abandon her and that she is not a good mother. She was a fantastic mother when "lucid", but would yell at us sometimes. In reality, we have had to distance ourselves to keep from being verbally abused when she does become upset. So it may seem to her that we are "abandoning" her. My brother currently cannot handle her at all as he is very emotional. So, I suppose he is temporarily staying away from her until he can figure out his life. I will occasionally try to hang out with her, but it is difficult and usually ends with her becoming very upset and yelling. She has stormed off on me a few times.
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She has been showing these symptoms for as long as I can remember, and I understand she is now a more extreme case to handle. It is almost daily that she will flip between calm and happy to upset and verbally abusive. She is very friendly, but is quite manipulative and creates drama quite often. She also believes in many conspiracy theories, and also believes that people are constantly out to get her. It is unfortunate because she is very smart, but cannot take any of her own advice on living a happy life because her emotions are so unstable. 

I would like to find ways to help by learning how to properly handle her. This will be in conjunction with therapy, and hopefully mood stabilizing medication later on. If she refuses to seek help I feel I will have to give her an ultimatum to decide between having no family or going to therapy. Currently it seems she will be seeking some therapy soon.

I have tried suggesting meditation to my mother, but she is not interested. Today I have told my father to start practicing meditation and inviting my mother in hopes of her participating with him. 
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UPDATE 1 - QUESTIONS FOR YOU:

1.) When and How did you, or the person you know with BPD learn about their disorder?

2.) What tactics have you seen work best for you to diffuse a situation as a person with BPD or arguing with  the person you know with BPD?

3.) How frequently do you or the person you know with BPD go into manic episodes? How frequently before and after treatment?

4.) How can family and friends best help people with BPD? (Boundaries are number one it seems.)

5.) How does someone with BPD finally accept that they have BPD once told by a professional? This question is for people with BPD specifically.
