Many people see 'original sin' as a depressing doctrine. I see it as refreshingly realistic and liberating.
This doctrine means that you don't have to pretend.
You don't have to pretend to be perfect: you are flawed. God knows it, and you can be pretty confident that the people around you know it too.
So there is no point in beating yourself up because you are not perfect. Instead, you can celebrate all the goodness and love and grace in your life - they are important, and they are also a real achievement. Being good is not easy.
And there is no point in spending your time in lengthy introspection. You are flawed - you won't find the answers you need there, whatever the New Age gurus may tell you.
And when you do something good, don't spoil it by looking too hard at your motives. You are flawed - of course your motives will be mixed. That does not negate the value of what you have done.
The wonderful thing is that God knows you are flawed. He doesn't expect you to be perfect. He commands us to feed the hungry; He does not command us to do it from perfectly selfless and altruistic motives. In fact, He promises to reward us for doing good - you can't even give a cup of water without getting rewarded. He knows what we are like, and He works with us the way we are.
This doctrine means that you can be reasonable in your expectations of other people. They are flawed, too. You may ask for perfection, but don't expect it.
The people around you will let you down sometimes, just as you will let them down sometimes. That's okay - it gives you and them the opportunity to practice forgiveness, and also practice receiving it.
Your children are human. They are flawed, just like the rest of us, and always have been. You may have let them down, disappointed and damaged them in all kinds of ways (being less than perfect, it is likely that you did) - but their problems are not all created by you and your inability to protect them from the world.
Some of their problems will be down to your mistakes, but possibly far fewer than you fear. Many of their problems are entirely of their own making; and others come from growing up in a fallen world. Even without you to let them down, they would still have been damanged; even if you had done a perfect job, they would still be flawed.
The other side of this doctrine is Original Goodness. The doctrine of Original Sin does not mean that mankind was originally created as sinful - it says precisely the opposite, in fact. We were created good - very good, according to God.
So the core of our nature is good. We may be flawed, but we are less than we could be. Greed and selfishness and cruelty are a part of the reality we have to recognise and deal with, but they are not the full or final reality. There is hope - not just hope that we can cope with the frustration and mess of normal life, but hope that all the things which limit and damage life can be finally overcome. In Jesus, we have the victory.