Is it permissible for the husband's father to control the life of his son and his wife, and why is the wife's father not entitled to the same control over his daughter's life?

Islam has made justice obligatory in all circumstances, and justice is incumbent upon everyone in all situations, and injustice is never permissible under any circumstances.

The term "control" [التحكم] is vague. The Sacred Law does not permit the husband's parents to abuse or wrong their son's wife. Obedience to parents is obligatory but not absolute; it has limits and conditions.

The difference between a son and a daughter in obeying parents after marriage is that a wife's obedience to her husband takes precedence over her obedience to her parents when there is a conflict.

Naming the child is the right of the husband. There is no problem with him obeying his parents in naming his child, and there is no injustice to the wife in that.