What is the ruling on a wife and children benefiting from the father's salary when he does not complete his official government working hours, and is the food they eat considered unlawful (haram)?

It cannot be definitively asserted that your father's salary is ill-gotten if his early departure was part of a common practice at work, approved by senior management.

However, if your father's departure was a deception and a dereliction of duty, then the money he receives for the hours he left work is unlawful (haram), and he should be advised gently to avoid the consequences of ill-gotten wealth.

Money earned unlawfully, such as the case mentioned in the question, is sinful only for the earner. It is permissible for the son to benefit from his father's money and spend from it, based on the fatwas of scholars.