God saved his family because he believed God's promise. Quite simple. And there are many more promises for Christians. Promises for EVERY problem a Christian will encounter.
God did not save his family because only he believed. God saved the family because the family believed.
The word says "Whosoever believes...shall be saved" not "whosoever believes shall be saved along with his family". My belief doesn't direct other people's beliefs.
As I pointed out already, I am receiving the blessings from God's promises. Does Satan bless? Of course not. My faith is stronger than ever, my children are blessed to have many Christian friends and resources, my husband has a thriving ministry teaching the word of God. I wake up and thank God, I go to bed thanking God.
God promises that He will take care of us. But that doesn't mean we just sit back and do nothing when problems arise. If we lose our jobs, we don't just say "well, God will give me another job" and do nothing. No, we search for a new job. When our car blows a tire, we don't sit back and say "God will rescue me" and then just wait. No, we either call for help or we walk to a nearby house. We take ACTION. Sometimes, the actions we take are the result of sin. That does NOT make the action itself a sin.
Also as I pointed out, in my remarriage, I've been able to show my teenager how a Godly husband and father should act. He's seen firsthand the benefits of God's blessings.
It makes me laugh that you still think I'm not a believer or that I won't inherit the kingdom of heaven, simply because I took ACTION over a sin that was consuming our lives. I took action with God's help and assistance. I was with God every step of the way and He took care of me during that time. Even when my ex tried to kill me, I didn't fear him because I knew God would handle the matter, and He was right there with me as I filed for a restraining order. I'll add that He even bumped the system for me because upon my divorce being finalized, the restraining order was made permanent - something I didn't even think about asking for but received anyway.
If you were separated for years, then I take it you have reconciled with your spouse. That is wonderful that you were able to do that and I applaud everyone who even attempts at reconciliation. That obviously is the best case scenario we can ask for, and when my husband is dealing with marital problems within the church he often takes a long time with reconciliation between the two parties. But reconciliation is not always possible, no matter how much you think it is. Sometimes, people have to be smart and understand that a situation is dangerous for them and for their faith.
I will always counsel abused spouses to remove themselves from the abusive situation, and then to take a long time working out whether their marriage can be salvaged or not. Sometimes it can, sometimes it can't. For those who have been wronged in their marriage, whether through infidelity or abandonment, and they no longer have a marriage, they still have the blessings of the Lord, as I have shown. Just because they didn't respond to the situation the way you think (and it is the way you think, not the way God thinks) doesn't mean they aren't believers or that they don't experience God's many blessings.