In a saner society stopping a fleeing criminal would be considered a “good thing”;letting them run away to try again means more crime.
I understand and sympathize with the mother’s reactions.
But I think a wiser way to deal with the situation, tactically, would be to take cover between the entry and the daughter, and blast him when he comes through the door.
Inside, she knows the terrain and the perp doesn’t. When she went outside, she exposed herself to the risk of there being more assailants, possibly armed, getting shot and leaving her daughter unprotected.
In this case, IMO anyway, protecting the daughter is infinitely more important than protecting the house.