Quote
My connection is that the believing wife or husband sanctify the unbelieving partner and their children by living such a Godly life that the unbeliever has no choice but to make a decision in favor of salvation in Christ. And that holds true for the children as well. They will see their parents living such Godly lives that eventually they will come to a saving knowledge of Jesus. This way, the faith can pass to the next generation. And it was by the works of the parents, indrectly, that led to their children being saved and thereby keeping the faith alive for another generation. Please let me know if I am wrong in this notion.

First, I don't really see how you're connecting these two passages. They're addressing two different subjects. Second, your conclusion is WAY off. Unbelieving spouses and children are made holy (set apart, different) by virtue of being intimately exposed to godly living and the means of salvation through the believing spouse. They are not holy because the unbelieving spouse and children will certainly believe due to the works of the believer! The unbelieving spouse who leaves is no longer "holy," nor grown children who depart from the home and the church. They have joined themselves to the world and so cannot be said to be "set apart."

Kyle

I tell you, this man went down to his house justified.