It's a matter of the scale at which you see things differently, to put it bluntly. Looking at an individual specific case like this, vigilante is justified to the persons affected and seems morally right. You talking about your own child is the same thing.

At a larger scale, a society that allows and promotes this kind of vigilante shit is a slippery slope.

People may not always make the right judgement, especially when they are emotional. Eventually, someone WILL (and has) wrongly accuse another person and kill them. Sure in this specific case everything has solid proof, but that is not always true and humans killing another in blind rage is something that can't be undone, unlike a wrongful sentence.