Self defense is covered by the ninth amendment. The Declaration of Independence states:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.—
The second amendment protects the right to the means of self defense, while the ninth protects rights not enumerated in the other amendments, which includes the right to life as enumerated in the Declaration.
To not even consider that the accused might have thought he was defending his and his child's life is pretty darn statist, IMHO. If nothing else the accused is supposed to be given the benefit of any reasonable doubt, of which there seems to be plenty in this case.
Negligent homicide is about the most severe case to be made, and even then you'd have to demonstrate that a reasonable person would have known the people breaking in were police.
Silently?
The Declaration of Independence states:
The Bill of Rights is in the Constitution.
The second amendment protects the right to the means of self defense,
Not murder.