Is a mother sinful if she does not tell her husband that the food he is eating was prepared by her sister, knowing that he has sworn not to eat her food, and what is the expiation for that?

There is no blame upon your mother for alerting your father, and she does not owe expiation for not swearing an oath. Nor does your father owe expiation for not intentionally breaking an oath, as Al-Nawawi mentioned that the predominant view is that there is no oath-breaking if the spoken or performed act that was sworn upon occurred due to duress, forgetfulness, or ignorance.