...OK, here's the nurse in me coming out....There is an odd syndrome called Munchausen's syndrome,which compels a mother to kill their child(ren) in an attempt to garner sympathy,and/or other rationalizations..
Münchausen syndrome is a psychiatric factitious disorder wherein those affected feign disease, illness, or psychological trauma to draw attention, sympathy, or reassurance to themselves. It is also sometimes known as hospital addiction syndrome, thick chart syndrome, or hospital hopper syndrome. True Münchausen syndrome fits within the subclass of factitious disorder with predominantly physical signs and symptoms, but in addition they also have a history of recurrent hospitalization, travelling, and dramatic, untrue, and extremely improbable tales of their past experiences. Nurses and doctors sometimes refer to them as frequent flyers, because they return to the hospital just as frequent flyers return to the airport. However, there is discussion to reclassify them as somatoform disorder in the DSM-5 as it is unclear whether or not people are conscious of drawing attention to themselves.
Münchausen syndrome is related to Münchausen syndrome by proxy (MSbP/MSP), which refers to the abuse of another person, typically a child, in order to seek attention or sympathy for the abuser. It is an obsessive want to create symptoms for the victim in order to obtain repeated medication or even operations.