First let's set this story back into its context.
David : 2nd king of Israel – known as the greatest king of Israel / 1000 BC –. David succeeded Saul. We are at the beginning of the kingship in Israel and it's quite strange in the Bible seeing that on arriving on the promised land, God means he doesn't want to name a king for his people. Men's government seem almost condemned as if it was rejecting God. We can read in the beginning of the book of Samuel “And the LORD told him (...) "They have rejected me as their king.” (1Samuel 7) and God warms Samuel on the dangers having a king. Still, God's people insists, they want a king to be like the other nations around them, and God eventually named Saul as their king, insisting on the fact that the king should obey the prophet speaking in the name of the LORD. But Saul failed & he didn't keep God's word so Samuel named David to be king instead of him.
We have a first interesting point here, which can help us to understand the story of David : Saul was chosen (by God)but then rejected – so you can be chosen and fail at a task for which you've been chosen (cf Judas) – No one is over anybody in this life, even a king can fail, and perhaps even the firmer believer – Matthew 11 :” Among those born of women there has not risen anyone greater than John the Baptist; yet he who is least in the kingdom of heaven is greater than he.” - Whoever we are in this life, we face the possibility of failing.
David indeed seemed to live a perfect life before God. He was a simple shepherd, the younger son of Jesse. He is chosen by the prophet and he began to win battles for Israel, however he remains honest to Saul and to his son Jonathan. Even when Saul tries to kill him, David forgives, doesn't take revenge and remains faithful to Saul.
So, is David going to be the perfect chosen one ? As a king ? As a believer ?

Reading this text, we could see that David isn't the perfect chosen one. His prophet, Nathan, comes to see him, as if he was asking an advice for some case, but we discover he's speaking of David's own case. What is it about ?
One day, David saw from the roof of his palace a young lady bathing. Her name was Bathsheba and she was married to Uriah the Hittite who was at that time fighting in David's army . David immediately wanted this woman and sent his servant to bring her back to him. Then, he slept with her, but she became pregnant. To hide his fault, David made Uriah come back to Jerusalem, hoping he would sleep with his wife but he didn't, so David gave orders to the chief of his army to put Uriah in danger so that he may get killed by the enemies, which happens. Then David takes Bathsheba to be his wife.
Nathan come to show his sin to the king. David has to face the truth, the horror he has made, he, the one elected by God. That's not little sins as you can see : it's adultery & murder ! David isn't a saint complaining about some imperfections, imperfection is not what we are talking about ! These are the worst sins, it's even worst than adultery and murder because David has probably raped Bathsheba and he made someone else kill her husband, one of his soldier fighting for him.
So, by a parable, Nathan is showing his sin to David (which he seems at first completely unaware of). So today, following his story we are going to ask ourselves how do we deal with truth, with the reality of our sins.

How does God deal with sin ?

God doesn't lead us into temptation. I know it's what we say in our prayer “lead us not into temptation” and temptation isn't sin : Jesus experienced it in the desert. But temptation may lead us to sin, temptation came from the evil. In Mark 1, 12 it is said “Jesus was being tempted by Satan”. We have to ask God not to permit us to be tempted because we must feel we are not always strong enough to resist.
God doesn't like us to be put in a situation of danger for our souls, that's also why he didn't want a king for Israel. Because he knows the risks of power, worshiping power, taking power on others men, and in fact that's David's sin : he abuses his power : Power is the root of sin, David is the rich man of the parable. He deals with other persons (Bathsheba, Uriah) as if they were simple pawns in the game. He plays God;
On the contrary God doesn't want to play God with us :God doesn't want us to obey without understanding. Nathan doesn't say to David “you didn't respect the rules” (adultery / murder) but he explains him his sin, showing by a parable what he did – he has to feel in his heart he hurt someone, he has to feel the pain he did to Uriah. God doesn't want us to respect the rules because he decided they were the rules, he doesn't accuse us but he wants to make us feel what sin is : lack of love, and lack of love always hurts.
Then God doesn't punish us. In this text, David's son die in consequence of his father's sin so we can wonder if God really kills David's son ? I don't think that when the OT was written people considered the babies as we do now, considering them as person in themselves. Here the baby is always referred to David so here I think we have to see the baby only as the fruit of sin. It means that we'll have to assume the consequence of our sins – Forgiveness isn't “magic” making everything disappears as if it was a (bad) dream. We have to understand in this story that the fruit of sin can't grow normally. So How does God deal with sin ? He tells us the truth (to David) / God is the truth / seeing God, we see the truth on our lives.

How does David deal with sin ?

David accepts the truth : at first, it seems that David doesn't understand anything about the parable and Nathan has to explain it to him.
First of all, Nathan reminds David about God : There is no mention of David thinking about God in all the story with Bathsheba and Uriah : David made as if God didn't exist, and the consequence is that he acted as if his neighbor didn't exist, didn't exist as a real person, a person you can hurt. Nathan has to remind David of human feelings, human way of being : justice, compassion. Sometimes it's more convenient to act as if God doesn't exist, as if our neighbor doesn't exist, denying their feelings, their sensibility, their love for us. Knowing the truth, realizing the situation, David mourns. Becoming aware of his sin, David doesn't say “alright, Lord I'm sorry, I won't do it again”. He understands he did something serious & God doesn't tell him “you've done wrong but it doesn't matter”. Evil gives birth to evil. David has to change something in himself to please God and to make things new in his life. He accepts the consequence of his sin and the pain of the sin : his son will die.
But David is confident and that's why he is first able to recognize his sin to Nathan. That's why he is also able to stop mourning after his child's death. He knows God truly forgives, truly loves us and can open the gates to a new future for us. On the other hand, Saul wasn't confident (1Samuel 13). That's why God rejected him finally. God can do nothing if we don't trust him. David knows God doesn't want to lock us up in our guilt – God doesn't like us to be sad but he wants us to change, to have a heart able to feel the pain of sin because only love can regret lack of love.
David takes a step forward : understand that God's love doesn't depend on our merits / learns to trust God. He may not be a “perfect king” but he surely can become a “holy king”. God doesn't want us to be perfect by our own strengths, making everything alright, but God wants to fill us with his spirit, with his holiness, with his love. He accepts us the way we are.

How do we deal with sin ?

The least we can say reading David's story is that it's not always easy to follow God ! We can be important in the eyes of men and feel very small in the eyes of God. We can try to love God but we discover our personalities don't change at once. Divine grace isn't magic. We still are sinners, are we aware of that ? How do we deal with sin ? I would like to point out from the story a few questions we can think of.
Do we “lead ourselves in temptation” thinking we'll be strong enough not to fail ? Are we walking in life like a king walking on the roof of his palace ? Are we sure of our power, even on of our power over sin, judging others people, not seeing what we've done wrong ?
Are we used to lying to ourselves, minimizing what we did, making arrangements with our own conscience ? Do we hide our sins or do we take the opportunity of being aware of them ? The Gospels are good books full of parables made to help us ! And if we get hurt, do we forgive other people because we are so perfect or do we forgive because we know we are sinners also ?
Feel the pain of sin – In a world which makes a diktat on being happy, can we still feel the pain ? Do we hear the word of “compassion” ? When I act, do I only think of myself, even thinking of “doing good” or am I able to put myself in other people's shoes ? Is it compassion that motivates me in my actions ? Do we wonder what is real love ? Can we call David's feeling for Bathsheba love ? In every situation, do we ask ourselves what we would do if we really loved our neighbor ?
Forgiveness : do we believe God loves us as sinners ? Or do we think God will love us only if we show a perfect face ? To sum up, I think a good question would be :How do we present ourselves to God : like the pharisee or like the sinner ? Luke 18 "11The Pharisee stood up and prayed about himself: 'God, I thank you that I am not like other men—robbers, evildoers, adulterers—or even like this tax collector. 12 I fast twice a week and give a tenth of all I get.'  13But the tax collector stood at a distance. He would not even look up to heaven, but beat his breast and said, 'God, have mercy on me, a sinner.'"

To conclude : when you are invited to reflect on your relations with other people, you can wonder what you are expecting from a relationship. Today we could wonder what we are expecting from our relation to God !
To become very rich, very powerful like a king, even if we want to be rich in wisdom or in kindness ! Do we expect that God will approve everything we do ? Or do we want to learn something from him ? Do we accept to be accepted as a sinner ? Needing God's love to make us grow in all our path of life ?
Assuming that, are we ready to take a step forward :
Understanding his sin, David learns to trust God but moreover David learns something about love Then he will be able to understand the sin of his son Absalom (which is presented as a consequence of David's sin). We can remember that Absalom will try to take the throne of his father and to show to people he's now the king he will take his father's wives. That's what Nathan alludes to in our text : verse.11 "Out of your own household I am going to bring calamity upon you. Before your very eyes I will take your wives and give them to one who is close to you, and he will lie with your wives in broad daylight”. But David keep his love for his son. When finally, Absalom is killed which enables David to come back to his throne, David will weep over his son, he will even say he would die instead of his sinful son : 2 Samuel 18 v 33 (learning his son's death) “The king was shaken. He went up to the room over the gateway and wept. As he went, he said: "O my son Absalom! My son, my son Absalom! If only I had died instead of you"" This means David really understood God's love because dying instead of us is what God did for us !
Are we able to feel the pain of lack of love ? Are we asking God to be able to feel it ? to feel like he feels about sin ?
So maybe to help us in this way, we could read again David's story and how his experience of believer speaks to us today.