I fell asleep last night thinking about the following possible scenario.
M is left to be the primary caretaker for her baby brother while mommy leaves them alone often and for extended periods of time. M is already well trained by mommy on how not to trigger her and be a good girl. Sky gets sick, tired, is whiny, crying while mom is out who knows where. M parrots what her mommy does and gives him medicine, vitamins, an herbal remedy? or does something trying to help but actually harms the baby because she is too young to know better.
JB comes home and M tells her how big of a girl she was helping her baby brother, who mom finds deceased. She hushes the girl off to bed, or another room, while telling M all along she did a good job. Mom then has to come up with something because she knows she's screwed and Sky's death is a result of an accident from neglect. She disposes of him, happens to see this particular episode of Law and Order SVU and decides that's the story she'll run with in the hopes everyone will buy it, she'll get a slap on the hand and retain primary custody.
I don't think she beat the kids. I simply think she was so engrossed in her compulsions she left the primary caregiving to her 4 yr old.
JMO