“So if someone one bruises or breaks bones on one of your family it is ok to kill.’
Depends, if it was an accident then no. Go about thinking your money is more important than my child and then you are responsible for your choices.
Have you considered the potential damage the robbers might do if they were not stopped? They already demonstrated an indifference to the persons and property of innocent citizens. If they get away, they have been rewarded for their actions.
It seems likely to me that the potential for future damage is far more if the robbers get away than if a citizen pursues them.
When the citizens are actively involved in stopping crime, and cooperative with the authorities it becomes very difficult for criminals to continue committing crimes against persons.