This is a very serious situation specifically because of her threats to harm herself and her child. I would strongly suggest that if she appears unstable and makes these threats (i.e. she states that she wants to harm herself or her baby) that you should call the authorities immediately. It would constitute an emergency situation. Get her to an emergency room or call the police and a mental health crisis team. The police or a mental health crisis team can come to the home and assess her mental health stability and the seriousness of her suicidal or homicidal statements. If they deem her to be a danger to herself or her child they’d have the right to take her to a hospital for further evaluation and treatment. I know this may seem harsh or like an overreaction but when unstable individuals are making threats to harm themselves or their children this needs to be taken very seriously. Please do not hesitate to involve the police or a mental health crisis team. They are trained to evaluate and handle those types of situations.
The other concern is that she may be using drugs. You remarked about the severe instability of her moods. This could be from, as you suspect, a possible psychotic episode but drug use could also explain these rapid mood swings. If she were using drugs this only further complicates the situation.
In summary, the best that you and your mother can do in this situation is to continually and vigilantly monitor your sister and her behavior. If she seems unstable or threatens to harm herself or her child please get her to a hospital or call the proper authorities immediately. As I mentioned above, this action on your part may seem like an overreaction but it’s not. There have been many unfortunate situations in which a suicidal or homicidal threat was not taken seriously and a tragedy occurred. It’s better to be “safe than sorry.” Your sister recently gave birth and then was left by her husband. This experience may have traumatized her and thus led to a psychotic break. It’s called postpartum psychosis. I cannot know whether you sister has postpartum psychosis but she might. When people are psychotic they are not thinking clearly. They often need help but cannot always recognize when it’s needed. Please see that your sister gets the help that she needs.