judgment call
It's easy to sit in one's armchair and pass judgment on what these officers "should have" done. It's quite another when you are faced with a deranged woman and a badly slashed child, are badly slashed yourself, and have literally seconds to react in order to prevent further violence.
Truly, even from the comfort of my armchair, I can find no grounds for criticism of these officers. Should they have attempted to use nonlethal force? Yes; and they did. Should they have waited until actual violence, as opposed to the threat of violence, occurred? That is questionable advice--but they did that, too.
This was, about as clearly as can be imagined, a "judgment call", and no one but the officers involved was in a position to make that call. If I had been in that room, I would not have had that right: it was not my job to deal with the threat, but theirs.
As Justice Oliver Wendell Holmes observed, "Detached reflection cannot be demanded in the presence of an upraised knife." that is particularly true in this case. With an enraged junkie with a knife standing over a child who may bleed out in seconds, one does not have the luxury of sitting down to think and plan. One must act, and NOW. Analyses given after the fact are irrelevant and, frankly, a bit precious.
Hoppy, I saw no comments about your mother, and nothing remotely resembling urine. I saw reasoned disagreement and nothing more, though sometimes emphatically stated. You said that you expected as much, and more, in your original post. Why complain when you get it? As my father told me more than once, "If you go looking for trouble, don't whine when you find some."