How can one atone for the sin of tearing money in front of one's father in a moment of anger, knowing that the father is psychologically ill, and reconciliation with him occurred later?

It is not permissible to tear money, as it entails wasting and corrupting wealth. The matter becomes even worse if the money does not belong to the one tearing it, and anger was the cause. As for repentance from this, it is achieved by regretting the action, resolving not to return to it, and increasing acts of seeking forgiveness. One must seek the father's forgiveness and strive for his satisfaction, and attempt to prevent him from violating the Shariah with wisdom and gentleness, without angering or insulting him.