First of all, good for her. That said, the article says that she and her son "chased him out of the house." I saw the news report last night, and the reporter said that they chased him out of the house and down the block to a wooded area where he stopped and they waited for police.
I don't know which is the more accurate reporting, but if it is the TV version, that was a big mistake. Police would have caught him anyway when he turned up at a local hospital for treatment of a GSW. In the meantime, the woman and her son had no idea if there was an accomplice waiting outside, or if said potential accomplice was armed.
If she chased the guy down the block into a wooded area and held him at gunpoint, that sounds very heroic.......but an accomplice could have killed her or her son if there had been one—which she had no way of knowing.
All the same, good for her for shooting the punk. Me? I'd have probably done the stupid thing too and hobbled after him with my cane, shouting "wait up! Wait for me!"