If my wife and children were being physically harmed or threatened, would I as a Christian be permitted to protect them? Or would I have to let them be harmed?

You would protect them, but without using violence. Even if it meant that you would be hurt in the process. Often when people ask forms of this question, there are unstated presumptions: (1) That we must meet violence with violence. Yet this shows a woeful lack of creativity. There are many ways to counter violence. And (2) that the most important thing is not to be hurt or die. And that justifies hurting others. Fortunately for us, this was not the way of Jesus Christ.