What is the fate of the son, and will the mother's custody of him be revoked, for fear of him being raised in a Sufi environment, this being after her husband divorced her three times, and she is influenced by her Sufi mother and brother?

Scholars have differed on whether immorality (fisq) revokes the right to custody. The Fatwa (religious edict) we adhere to is that it does revoke it.

However, in this specific case, consider the child's condition and age. If the child is young and does not comprehend heresies, then do not take him away from his mother. But if he has reached an age where he can comprehend them, then you must take him away from her, lest he be influenced by them. This is based on what has been narrated in the words of the Hanafis: that a Dhimmi woman (non-Muslim living under Islamic rule) and an immoral woman have a greater right to custody as long as the child does not comprehend religions.