First, it’s a black bear, they’re just as scared of you as you are of them.

Second, once the kids were safe in the house and the bear ran up a tree there was no need to keep shooting at it.

Shooting a bear in your garage is self defense. Chasing it and shooting at it once it’s out of your house is no longer self defense.

Same rules here for lethal force against people. Someone breaks into your house? Fair game. Outside your house? Not so much.