How should a Muslim woman's relationship with her former husband's father be regulated, and is she required to observe hijab in front of him?

The husband's father is a mahram (definition) to the woman immediately upon the marriage contract, even if her husband divorces her, due to the Almighty's saying: "and the wives of your sons who are from your own loins." This is the mahramiyyah (prohibition of marriage) established through affinity. Those prohibited by affinity are of four types: the wives of the father (the father's wife and the grandfathers' wives), the wife's mother and her grandmothers, the stepdaughter (the wife's daughter from another man) if he has consummated the marriage with her mother, and the son's wife and the grandsons' wives.