I'm very sorry to hear of the situation. It is impossible to diagnose someone via JustAnswer but based on your description I would seriously consider the possibility of Borderline Personality Disorder (BPD). BPD is often mistaken for a mood disorder due to the frequent mood swings but the variation is too quick (days rather than weeks) and the instability tends not to respond to antidepressant medication. Self harming is a hallmark of BPD and we often see it develop in people who have experienced a difficult/traumatic relationship with a parent. Multiple hospital admissions due to crisis is also a hallmark of BPD.
I would suggest that you ask her current Psychiatrist if he/she has considered BPD and if so why this diagnosis has been discounted. If you don't get a satisfactory answer (either way) then I would strongly encourage her o get a assessment done by a clinician who is experienced in working with BPD.
I'll place a description of BPD here for you to look through. Keep in mind that every feature does not need to be present/occurring.
The main feature of borderline personality disorder (BPD) is a pervasive pattern of instability in interpersonal relationships, self-image and emotions. People with borderline personality disorder are also usually very impulsive. This disorder occurs in most by early adulthood. The unstable pattern of interacting with others has persisted for years and is usually closely related to the person's self-image and early social interactions. The pattern is present in a variety of settings (e.g., not just at work or home) and often is accompanied by a similar lability (fluctuating back and forth, sometimes in a quick manner) in a person's emotions and feelings. Relationships and the person's emotion may often be characterized as being shallow.
A person with this disorder will also often exhibit impulsive behaviors and
have a majority of the following symptoms:
Frantic efforts to avoid real or imagined abandonment
A pattern of unstable and intense interpersonal relationships characterized by alternating between extremes of idealization and devaluation
Identity disturbance, such as a significant and persistent unstable self-image or sense of self
Impulsivity in at least two areas that are potentially self-damaging (e.g., spending, sex, substance abuse, reckless driving, binge eating)
Recurrent suicidal behavior, gestures, or threats, or self-mutilating behavior
Emotional instability due to significant reactivity of mood (e.g., intense episodic dysphoria, irritability, or anxiety usually lasting a few hours and only rarely more than a few days)
Chronic feelings of emptiness
Inappropriate, intense anger or difficulty controlling anger (e.g., frequent displays of temper, constant anger, recurrent physical fights)
Transient, stress-related paranoid thoughts or severe dissociative symptoms
Key Features in Detail
Frantic efforts to avoid real or imagined abandonment
The perception of impending separation or rejection, or the loss of external structure, can lead to profound changes in self-image, emotion, thinking and behavior. Someone with borderline personality disorder will be very sensitive to things happening around them in their environment. They experience intense abandonment fears and inappropriate anger, even when faced with a realistic separation or when there are unavoidable changes in plans. For instance, becoming very angry with someone for being a few minutes late or having to cancel a lunch date. People with borderline personality disorder may believe that this abandonment implies that they are "bad." These abandonment fears are related to an intolerance of being alone and a need to have other people with them. Their frantic efforts to avoid abandonment may include impulsive actions such as self-mutilating or suicidal behaviors.
Unstable and intense relationships
People with borderline personality disorder may idealize potential caregivers or lovers at the first or second meeting, demand to spend a lot of time together, and share the most intimate details early in a relationship. However, they may switch quickly from idealizing other people to devaluing them, feeling that the other person does not care enough, does not give enough, is not "there" enough. These individuals can empathize with and nurture other people, but only with the expectation that the other person will "be there" in return to meet their own needs on demand. These individuals are prone to sudden and dramatic shifts in their view of others, who may alternately be seen as beneficent supports or as cruelly punitive. Such shifts often reflect disillusionment with a caregiver whose nurturing qualities had been idealized or whose rejection or abandonment is expected.
There are sudden and dramatic shifts in self-image, characterized by shifting goals, values and vocational aspirations. There may be sudden changes in opinions and plans about career, sexual identity, values and types of friends. These individuals may suddenly change from the role of a needy supplicant for help to a righteous avenger of past mistreatment. Although they usually have a self-image that is based on being bad or evil, individuals with borderline personality disorder may at times have feelings that they do not exist at all. Such experiences usually occur in situations in which the individual feels a lack of a meaningful relationship, nurturing and support. These individuals may show worse performance in unstructured work or school situations.
As medications tend not to have much effect on BPD the treatment generally regarded as the best approach to BPD is Dialectical Behavior Therapy (DBT). DBT is a system of therapy developed specifically to treat persons with borderline personality disorder. DBT combines standard cognitive-behavioral techniques for emotion regulation and reality-testing with concepts of distress tolerance, acceptance, and mindful awareness largely derived from Buddhist meditative practice. DBT is the first therapy that has been experimentally demonstrated to be effective for treating BPD.
DBT is usually offered by Clinical Psychologists (although not exclusively) and you can contact The Australian Psychological Society for assistance with finding an appropriately trained Psychologist. Take a look at the APS locator service here - you can use this to find a Psychologist in your area and there is a phone number you can contact if you want a referral arranged for you. Also, take a look at an article published by the American Psychology Association here. It's an interview with a senior Psychologist and covers some of the things you should consider when you looking for a Psychologist. You should also be aware that Medicare subsidizes sessions with a Psychologist in many circumstances, so you may be able to get some help at little to no cost to yourself.
There are a number of books that can assist people to learn Dialectical skills at home and to generally manage typical Borderline behaviors. If you are interested in doing some further reading I can recommend both this book here and this book here .
I hope this has been of some help. Please let me know if you have further questions or wold like me to clarify any part of my answer.