I'm going to assume you are discussing in good faith.
Yes, it is the policy's responsibility to enforce the law. But they are also not supposed to escalate or use unequal force. Jumping in front of a moving car is "dont do this 101." She had diapers in her car and was trying to get away, not hurt people. In this case gunfire is never an appropriate and justified force. If she had a bomb in her car and said "I'm going to go blow up the elementary school" and sped off towards the school, I'd understand using lethal force to stop her.
Your home invasion part created a lot of unnecessary arguments. In most states, if you shot someone fleeing in their car when they were no longer threatening your life, you'd be convicted of murder. You then conflate accepting an attack on you with shooting someone that was clearly fleeing because they previously threatened you. I'm also not sure why you even brought up shooting an 8 year old running across your yard, that isn't relevant to this situation and I think everyone can agree that's wrong no matter what, no matter how old the person is.
It doesn't matter if states laws are nonsensical, and that's kind of the point. You also confuse what you're willing to accept to do to protect your family with what is legal. In some states you have a duty to warn them or allow them to retreat if they are not directly threatening you, and being in your home unlawfully is not automatically threatening you.
Your emotional conviction to protect your children is not being argued. The point was that even in a situation, where a civilian such as yourself fears the safety of their children, you could have a duty to warn or allow an invader to flee your house depending on the state you live in. While a trained and professional police officer escalated a nonlethal situation by jumping in front of a moving vehicle, and then further escalated it by using lethal force and murdered a person. Even worse, it was legally "justified" despite being completely unreasonable.