Must I repeat the expiation if I appointed my cousin to feed 60 needy persons, and he bought meat and distributed it to only 30 people?

What your cousin did was wrong, for he should have fed sixty poor people from the average of what you feed your families, or distributed its value to them. He should not have sufficed with distributing meat to thirty poor people, as paying atonement to fewer than the specified number is not valid according to the majority of scholars. You must complete the atonement by feeding thirty more poor people, and your cousin is responsible for what he gave to those who were not deserving, unless you forgive him. We also note that expiation through feeding is only valid after being unable to free a believing slave and unable to fast for two consecutive months.