What should I do regarding my family who mistreated my wife and caused the spread of abuse about her, which negatively affected my life and my relationship with them, and should I boycott them?

If you are wronged, rejoice in the companionship and support of Allah. Continue to uphold kinship ties and be dutiful to your relatives, even if they sever ties with you and treat you poorly. Endure and be patient, and respond to ill-treatment with kindness; for that may open their hearts and transform their enmity into love. As for those who accuse your wife of what is unbefitting, they have committed something forbidden, and they must repent and seek forgiveness. This does not justify your disobedience to your mother or diminishing her status.