As you consider using life's circumstances to disciple your children, remember that there are three ways you can do this. Modelling, observing and responding. 
Modeling is most important. The way that you respond to life in front of your children will do more to shape them than any instruction you may give. This is why it is essential that we have a faith that is motivating our obedience in all of life personally. No matter how busy you are, don't stop making regular time to fellowship with God privately and take every opportunity you can throughout your day to direct your thoughts back to Jesus and the wonder of all he has done for us. May your daily delight in him be evident to all. 
Then we can observe what is happening in the world around us, when we see or hear of something together and when our kids come home and tell us about their experiences. We can point out the sin, suffering and celebration that we see around us and in our own home. 
And we can respond to all of these things, simply and lovingly, with God's truth. Not lectures. Not condemnation. Just simple comments, thoughtful questions, genuine prayers. 

You may have many opportunities for conversations with your children in your lifetime. Use them well. 

Before we ever hope to teach our children to respond rightly to sin we must ask ourselves: what is my attitude towards sin?
Do you have a clear understanding of what the Bible teaches on sin? Do you accept that you are personally a sinner still in need of daily grace, even as you live as a Christian? Do you take regular opportunities for confession and repentance?
This is where we must start. When these things are on track, our children will naturally learn these principles from us as they see us live them out in our own lives, as we lovingly guide them through their own struggles with sin and as we see the effects of sin play out in the world.
The Bible has much to say on sin, so take the time to study this topic if you haven't already. You may find some of the resources below helpful to supplement your study of God's Word.

Paul Washer - The Depth of the Gospel Part 1 - The Master Seminary - YouTube

Do Christians Still Have Evil Desires? | Desiring God 15 minute audio by John Piper

Kill Sin or Sin Will Kill You: Battling Unbelief - YouTube 

"Overcoming Sin and Temptation," by John Owen. The version edited by Kelly Kapic is quite a challenging read, but worth it if you can manage. Puritan Paperbacks has a good abridged version available, called "Indwelling Sin in Believers."

Suffering can be broadly defined as having something you don't want or not having something you do want. The Bible has much to say on this topic, but sometimes the comforts of modern life can lead us to be unprepared to face suffering when it does inevitably come.
So what about you? Do you have a clear understanding of the Biblical repsonse to suffering? Not to say that you have all the answers for all the facets of suffering that we face today, but as you face suffering in your own life, does it pull you towards God and his truth, or away from it?
Our kids will face suffering, large and small, in this life, and it is a wonderful privilege for us as parents to equip them to deal with suffering well. May we do this as they see us face suffering. May we do this as they face small, insignificant sufferings, that this would set the ground work for greater challenges to come. May we do this so we can rejoice always, pray without ceasing and give thanks in all circumstances; for this is the will of God in Christ Jesus for you (1 Thessalonians 5:16-18).
If you would like to grow more in your understanding of and response to suffering, as you walk through it personally and guide your children through their own, there are many great Bible passages to meditate on. For further study, see the resources below.

How Our Suffering Glorifies the Greatness of the Grace of God - YouTube

What Is the Secret of Joy in Suffering? | Desiring God  Short article by John Piper

The Terrible Truth: Suffering Is Not For Nothing with Elisabeth Elliot - YouTube  The first in a seven part series on suffering.

Worth Every Second: Vaneetha’s Joy in Suffering - YouTube a short, powerful testimony of one woman's suffering and God's work through it

 Though You Slay Me A great song on this topic, by Shane and Shane, featuring John Piper

We are made to experience pleasure in so many ways-from relationships, food, activities and more. So how do we respond to the good gifts that God gives us every day? Even the smallest of happy things can be an opportunity to point our hearts back to him in praise and thanks.
But do we?
What wonderful, bountiful opportunities come our way everyday for us to delight in, praise and thank God for his provision to us. Even at times when our hearts are too caught up in a good gift, we can thank God for it, but take the opportunity to remind our hearts that he is the greatest gift we have been given through Christ, he is the only one who will satisfy all the longings of our souls.
The Pslams are a wonderful source of passages that rejoice over God's goodness to us and provision for our needs. There is also a great article by John Piper,  How to Drink Orange Juice to the Glory of God | Desiring God which gives a great practical example of this. 

The principles of Ephesians 6:4 apply again here. As we grow in our own understanding of the Biblical response to sin, suffering and celebration, and in our desire to share these wonderful truths with our children, we should be cautious. There are ways of doing this that will provoke our children to anger; if we talk too much or too often of these things. Much prayer and discernment is needed. May we be authentic in our sharing with our children, doing it in a way that would please the Lord, not out of a desperate need to form their minds biblically, but from the calm, joyful assurance that in all of life's circumstances, there is great opportunity to delight in God.