As an ex Law Enforcement Firearms Instructor, I ask you to at least remember this before touching that trigger:
Are you 100% convinced, that you, or another innocent human being, is in immediate danger of great bodily harm, or death? If NOT, then do not touch that trigger or point your muzzle at another human being. Period. It's that simple.
Castle Doctrine is another layer to this, but we are not talking about defending property here and laws vary in different jurisdictions regarding the use of deadly force in the defense of property.
Even in Agorism and Anarch*, we absolutely agree that defense of a human life is justified, up to and including the use of deadly force if it is justified. Meet force with equal force, NEVER escalate a situation. Non-Aggression Principle (NAP).
Remember this... You are going to have to explain to one or more people, and convince them, why you killed a human being.
RE: Children vs. Grownups