I would expect that officer to shoot to stop the threat, period. I would expect him to shoot at the center mass of my loved one's body in order to stop the threat he/she would be presenting to the kids. Deliberately aiming at someone's limbs (arms or legs) is stupid for multiple reasons. One, limbs are in motion at a greater speed and more angles than the torso, vastly increasing the chance of missing and the shot going wild. Also "winging" them does not necessarily stop the threat. Intentionally wounding someone with a lethal weapon opens up a huge vista for the trial lawyers association creative lawsuit division to sue.
A reasonable person might conclude that although a psychotic man with a knife might justify lethal force, the situation by definition does not require it, and that lethal weapons do not require lethal use.
You need to study up on force theory. If lethal force is justified, it is by definition, necessary. If it is not required, it is by definition, not justified. You can't use a lethal weapon in a non-lethal manner without serious civil and legal ramifications for excessive use of force. That's how it works in real life no matter how silly Hollywood gets with movie plots.
You expect so very little of the police. How very, very sad.
God I hope that you aren't an LEO. Your ideas on "the requirement" to use lethal force are not only illogical, they constitute de facto murder of the insane.