What is the ruling of the Sharia on shunning a sister after she becomes pregnant by a young man, and is there a sin upon the one who shuns her for that, and how can the heart find peace from this feeling?

If your sister has repented from immorality, then it is not permissible to abandon her. However, if she persists in sin, then it is permissible to abandon her, while considering what is most beneficial. If abandoning her will help her return to righteousness, then that is preferable. And if maintaining ties and offering advice is more beneficial, then that is preferable. The marriage of two fornicators is not permissible except after repentance and the delivery of a pregnancy or purification (istibra'). The child of fornication is not attributed to the fornicator according to the majority of scholars.