YOU SAID:
My cat has a dog who likes fish to eat
INTO JAPANESE
私の猫には魚が好きな犬がいます
BACK INTO ENGLISH
My cat has a dog that likes fish
INTO JAPANESE
私の猫は魚が好きな犬を飼っています
BACK INTO ENGLISH
My cat has a dog that likes fish
That didn't even make that much sense in English.