Honestly that story doesn't sound very good to me. It seems like he believed he was entering an empty house. When he opened the door to where her and her kids were she just started shooting and as he begged her to stop she continued shooting. I think a verbal command is in order first. "Stop! Get out of my house of I'll shoot you!" If he doesn't stop or makes any sort of sudden movement go ahead and shoot. If he leaves let him leave. The gun might have been able to save her and her kids' life without her shooting a man in front of her children.
I think I agree with you here, in the most basic way of "wouldn't it be nicer to solve the problem without shooting if possible" sense.
however, the woman was terrified. . . . and a lot of people are just going to be terrified, particularly women and kids, when someone breaks into their homes.
I think the burden of having "good sense" or "good manners" should be left on the perp who trespasses, breaks and enters, or initiates the offense. . . . as long as he is advancing. When he starts to flee the threat just isn't the same. . .
but this woman was cornered, and the terror was understandable. It would have been better if she had listened and stopped firing, but I'm not sure I want people like her becoming the defendants in court. I'd say when you enter unlawfully into others' property and present a threat to their safety, it's like you have pulled a gun on somebody, and if they shoot back it's all self defense. Boy I hate courts sometimes when they get hung up on trying to make people offenders for their inability to keep a cool head when feeling their lives are on the line.