Is it permissible for my wife to cut ties with her brother who does not pray, is undutiful to his parents, and whose wife goes to sorcerers, especially after he insulted her and us on Facebook, and she refused to reconcile with him to avoid his and his wife's behavior?

The couple should be advised to repent from their wrongdoings. If they repent, it is not permissible to abandon them. However, if they persist in disobedience, and abandoning them serves as a deterrent, then abandonment is permissible. If they are harming the wife, and their harm cannot be averted except by abandoning them, then there is no sin upon her for abandoning them. Nevertheless, her patience and diligence in advising them and striving for their rectification are more preferable.