Captain, I don't know about everyone else, but I still am perceiving the entire issue as relevant to writing. We are very unlikely to come upon such a situation in real life, but we are very likely to want to present moral dilemmas such as this in our writing (at least I am!) so I'm trying to figure this out for writing purposes, so I humbly submit that this discussion is still quite relevant.
Astronomer wrote:
I'm confused. How is salvation not relevant to this question? Surely the entire Bible is focused on how we can more closely follow after Jesus and, in doing so, bring others to follow after him as well. Surely salvation is a prominent point in scripture. Or am I just twisting your words out of context?
Yes, I agree with you that that is the Bible's purpose. And just as you say, it's not only about causing others to follow Him, but ourselves following more closely after Him. So it's not just about saving the life of someone who may not be a Christian. In saving the life of the Christian, you may be saving someone that God is going to use far more than you could ever imagine, someone who will bring millions to Christ. And in saving your children, you're saving those whose spiritual growth you are personally responsible for. So it seems to me that it's irrelevant to this decision, as we cannot know what God's plans are for each person.
As Robert E. Lee said: "Duty is ours. The consequences are God's."
So I submit that we must figure out our duty, and let the question of salvation and the future rest in God's hands.
Have I explained myself more plainly this time?

The family is the first earthly institution, and each man's family is the group of people that God has specifically placed under his care and guidance. Yet the Bible also says that God establishes rulers, placing the people of the kingdom under each ruler's care. They are to punish evildoers, reward those who do well, and protect the innocent.
One thing I've been doing to study this issue is noting the actions of the kings of the Bible. One sad fact I've noticed is that none of the good kings seemed to be very good fathers. David, Solomon, and many of the lesser-known kings of Israel all had their families pretty much fall to ruin. Consider especially David's actions with Absalom. He was chided for preserving Absalom at the cost of his kingdom, and though Joab was not the voice of God, the Bible seems to confirm his words, since David later admitted his wisdom. But it's a puzzling story, and a hard one to sort out right and wrong, since the Bible neither expressly condemns nor condones what happens.
It's certainly hard to figure out, but at this point I'm leaning towards that God wants a leader that He has established to put the country first. But I can see arguments on both sides, and am not yet sure.
(Wow, that is the longest post I've written in ages...)