the farmer saying he treats the animals like family, which one might imply means he treats them well. but his family has to secretly run away from him due to abuse (insinuated by the wife quickly leaving with the kids). this mean he probably also abuses the animals, which is opposite of the implied meaning.
if it said something like “Farmer: i treat my family like my animals” then i would agree with your interpretation that his family now thinks they will be slaughtered. but it being flipped changes the meaning for me