You misunderstand what the Church teaches. Penance does not atone for anything. After the sin is forgiven in a sacramental confession, the priest assigns penance for the benefit of the penitent, but the sin is forgiven the moment the priest absolves it, and not after the penance is done. This is a common misunderstanding.
Then someone needs to correct Ludwig Ott, John Hardon and a host of other Roman Catholics, including the Council of Trent because that is exactly what they state of penance, being the atonement or reparation or expiation of sins committed after baptism.
Penance is a sacrament of the New Law instituted by Christ in which forgiveness of sins committed after baptism is granted through the priest's absolution to those who with true sorrow confess their sins and promise to satisfy for the same....
the absolution given by the priest to a penitent who confesses his sins with the proper dispositions remits both the guilt and the eternal punishment (of mortal sin). There remains, however, some indebtedness to Divine justice which must be cancelled here or hereafter (see PURGATORY). In order to have it cancelled here, the penitent receives from his confessor what is usually called his "penance", usually in the form of certain prayers which he is to say, or of certain actions which he is to perform, such as visits to a church, the Stations of the Cross, etc. Alms, deeds, fasting, and prayer are the chief means of satisfaction, but other penitential works may also be enjoined. The quality and extent of the penance is determined by the confessor according to the nature of the sins revealed, the special circumstances of the penitent, his liability to relapse, and the need of eradicating evil habits. Sometimes the penance is such that it may be performed at once; in other cases it may require a more or less considerable period, as, e.g., where it is prescribed for each day during a week or a month. But even then the penitent may receive another sacrament (e.g., Holy Communion) immediately after confession, since absolution restores him to the state of grace. He is nevertheless under obligation to continue the performance of his penance until it is completed.
If you have specific questions about Ott, Hardon, or Trent, don't hesitate to post the material that troubles you, and ask.