Who among my relatives is permitted to shake hands with my wife and look at her, given that she is fully veiled?

Marriage establishes a state of mahramiyyah (unmarriageability) between the wife and her husband's fathers, whether by lineage or suckling, based on the Almighty's saying: "And let them not display their adornment except that which is apparent thereof; and let them draw their headcovers over their bosoms, and not display their adornment except to their husbands, or their fathers, or their husbands' fathers." And a grandfather is considered among the fathers. So, the husband's father and his grandfather from the mother's side are mahrams to the wife. It is permissible for her to shake their hands and be in seclusion with them if there is no fear of fitnah (temptation).