Women "Innocent" if They Kill their Own Children?

This week, a 25-year-old mother from Texas hung herself and her four children, one of them survived:

A young mother who may have been depressed apparently hanged three of her small daughters and herself in a closet using pieces of clothing and sashes, authorities said Tuesday.

A fourth child, an 8-month-old daughter, was also found dangling in the closet but was rescued from the family's mobile home.

The article ends up with some observations about four other Texas women who had killed their children. All four of those women were found "innocent" by reason of insanity.

Compare these cases of women who kill their own kids with a recent one for a Texas babysitter who is to be executed next month:

But just weeks after Henderson started working for the Baughs, 3-month-old Brandon was dead and Henderson had fled the state. The infant's body was found buried 60 miles away with his skull crushed, wrapped in his yellow-trimmed white blanket and stuffed into a box that previously held Bartles & Jaymes wine coolers.

Henderson, 50, is set to die in less than three weeks for the 1994 slaying that made her one of the most hated women in Texas. She would be just the 12th woman among the nearly 1,100 convicted killers executed since capital punishment resumed in the United States in 1977....

Henderson insists Brandon died in an accidental fall and that her decision to bury him and flee was made in panic, not in cold blood.

My question, why the "lighter" sentences for killing one's own kids vs. killing another woman's? Is it because children are seen as women's property so it is "okay" to kill one's own but not another woman's? If so, isn't this a little sick?

Also note how few women are actually executed at all. They make up 10-15% of homicide offenders but only 1% of executions have been women.