Do I have this right? (SPOILERS)

What I think is:

The wife (Julie?) has postpartum psychosis, causing her to have an intense 'hate' of the baby(cringing when he cries, not wanting to touch him; care for him; or be in the same room with him, getting overly upset when her husband even mentions the baby to her, thinking he hates her, many periods of crying, attempted suicides, many stillborn babies).

Obviously she spoke with a doctor about this and was diagnosed wrong (postpartum psychosis is very rare).

The husband (Frank?) checks in on the baby a lot more often than the average baby because he doesn't trust his wife.(scares in the past perhaps? Women with postpartum as severe as hers tend to make more than one attempt.)

Julie freaks out and kills the baby "I never touched him, not the way a mother should" (I think shaken baby syndrome via the cradle as was shown in the video monitor) then runs off and accidentally falls. The necklace came off in her violent shaking because of the force she put into it.

Frank finds the dead baby and freaks out because his baby is dead (suspects wife?); he can't take the pressure of his son's death, after all of the stillborns and his wife's issues, and mentally snaps. He 'daydreams' the family safe and cares for the baby (thinking nothing off with his wife not wanting to help much because she never did before), 'finding' her with the sliver in her arm and seeing her with the blood and 'gunk' all over the left side of her face because he cannot think that she is dead and wants other explanations.

Frank 'knows' that his son is dead and that's why he always leaves him alone.

Julie's ghost comes back because she want to love her son 'right'.

Helen is not that important in the story, just a bystander who gives him a 'better' explanation than the one he has (sister's spirit returned as compared to wife killed the baby). Sam reminds her of what happened to her sister and that throws her into a panic, she also is searching for an answer to why the babies died (she thinks it's the sister because to her it is the only logical explanation as opposed to the mothers having something wrong or her doing something wrong).