Are the husband and the wife's family sinful due to their refusal to break the fast with the husband who intentionally broke his fast during the day in Ramadan? And what must they do to atone for this sin?

Breaking the fast in Ramadan without a legitimate شرعي excuse is a major sin. The travel that permits breaking the fast is approximately 70-80 km. As for being at home or in the suburbs of a town, that is not considered travel, and breaking the fast in such a situation is a major sin. Whoever aids someone in breaking the fast without a legitimate excuse shares in the sin, for Allah Almighty says: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression). The fast remains valid, but aiding in such an act is a sin and requires repentance. Whoever orders his wife or daughter to prepare food for someone breaking the fast without a legitimate excuse must repent. The wife or daughter would be doing well by disobeying him, for the Prophet ﷺ said: (Obedience is only in what is good) and (There is no obedience to a creature in disobedience to Allah). It is not permissible to aid a husband in what Allah has forbidden, and obedience to Allah takes precedence. Whoever intends to stay in another town for more than four days is obliged to fast. However, if the stay is four days or less, he may break the fast if he is a traveler, but fasting is better.