Training your Chlidren in the way they should go

So obviously I don't have any children yet, but in my reading lately I have noticed something interesting on the subject. So, all of us that are home-schooled are exposed to the fact that fathers (and mothers) need to train their children in the Lord, having discipleship and teaching character.
But the thing I've notice is that there are some great men in the Bible that are respected and well known, but somehow some of their children rebelled. Now I'm not saying that well raised children are guaranteed to stay on the narrow path. So, I'm saying that it looks like they (men in Bible) had neglected the training up of their children.
So here are the example's I've come across....

1. Eli's (the priest) sons were rebellious and eventually the Lord killed them; this is the Eli that trained up the little Samuel to became a great men for God. So I go what happened with Eli's sons?
But even though Eli rebuked them for their behavior, he did not discipline them. He was the high priest at the time and had the authority to at least remove his sons from priesthood until they repented. But he didn't.

2. Another example is King David. He also had a son that rebelled. What happened to him? In the text it says that Absolum (spelling) was 'handsome', maybe David thought he had this cute little boy that couldn't do anything wrong (or didn't have the heart to discipline) until, when he got older he rebelled and David almost lost his kingdom. I don't know for sure what happened, but something to learn from.

3. And then also Arron's sons in Leviticus did something that displeased the Lord and were 'consumed' by the Lords fire.

So whether it was a father who was slacking in his job or just some rebellious sons, I don't what to be either one of them. Either right now or in the future.
So that's my two cents of what I've learned this past couple of days.