How can one repent and atone for the sin after engaging in an unlawful relationship with a married female relative, and what is the way to avoid Allah's punishment upon one's family and future wife?

It is obligatory to hasten to repent to Allah from a forbidden relationship. Repentance is achieved by abandoning the sin, regretting it, and resolving not to return to it, while maintaining secrecy and not publicizing the sin.

Among the things that help in repentance is to hasten to marry a righteous woman if you are able, and there is no objection to marrying the woman with whom you had the relationship after her waiting period has ended.

If your repentance is sincere, then rejoice in its acceptance and do not fear punishment, for "one who repents from a sin is like one who has no sin," and a penitent person will not be punished in this world or the Hereafter.