YOU SAID:

My mom went to the store and back, but she had to go slow because it was raining cats and dogs

INTO JAPANESE

私の母は店に行って戻ってきましたが、猫と犬が雨が降っていたのでゆっくりと行かなければなりませんでした

BACK INTO ENGLISH

My mom went to the store and came back, but the cat and dog were raining so I had to go slowly

INTO JAPANESE

お母さんがお店に行って帰ってきたのですが、猫と犬が雨が降っていたのでゆっくり行かなければなりませんでした

BACK INTO ENGLISH

My mom went to the store and came back, but the cat and dog were raining so I had to go slowly