"If it were you...what would you do? Borderline Personality Disorder has drained me mentally, and she's not cooperating with me at all..."
"It's perfectly normal for her not to cooperate, instability is a characteristic of Borderline Personality Disorder. Using threats of suicide to manipulate important people in her life is a typical diagnostic trait, isn't it? If she threatens you with suicide, it means you're already important to her. What you need to do now is give her a consistent and stable emotional connection, let her know that you value her, prove it over and over again, until she truly believes that you also value her. This might take a long time, but during this time, not only will her condition improve, you'll find yourself too, isn't that great?"
Being a psychologist is a very tough career.