A; I can’t make a diagnosis on the basis of a letter, of course. And the label doesn’t really matter anyway. What matters is that your sister is in great pain and her methods of coping are hurting the very people who love her. You didn’t mention whether any of these behaviors were present before she lost her baby so I don’t know if the root of the problem is the trauma of that loss or if the loss exacerbated already existing problems. Either way, she does need help. I’m especially concerned about the effect of her behavior on her children. I wonder what they make of their mother’s chronic anger and sorrow. Do they feel that they aren’t enough? Do they feel guilty that they are alive while their sib is dead? Do they wonder if she loves them as much as the child she lost?
Unfortunately, you can’t make your sister get the help she needs. What you can do is educate yourself about how people manage the loss of a child and what causes some people, like your sister, to get stuck in the grieving process. You would then have new information to share with the rest of the family. My guess is that they (and you) have felt as stuck as your sister. If you all had some idea of what to do, you might be able to respond differently. If you think the children are in danger of neglect or emotional or physical abuse , you need to get child protective services involved. They might pursuade her to accept some support for the sake of her living children.
I’m sorry you’ve been the lightening rod for her pain. Please don’t take it personally. Whatever the reason, that probably won’t change unless she finds some peace so you’ll need to work quietly behind the scenes. I’m impressed that you are able to love her in spite of it all.
I wish you all well.