YOU SAID:
I walked down the street, smiling at my distant mother.
INTO JAPANESE
私は遠く離れた母に微笑みながら通りを歩いた.
BACK INTO ENGLISH
I smiled at my mother who was far away as I walked down the street.
INTO JAPANESE
通りを歩いていると、遠く離れた母に微笑みました。
BACK INTO ENGLISH
As I walked down the street, I smiled at my mother in the distance.
INTO JAPANESE
通りを歩いていると、遠くにいる母に微笑みました。
BACK INTO ENGLISH
Walking down the street, I smiled at my mother in the distance.
INTO JAPANESE
通りを歩いていると、遠くにいる母に微笑んだ。
BACK INTO ENGLISH
As I walked down the street, I smiled at my mother in the distance.
INTO JAPANESE
通りを歩いていると、遠くにいる母に微笑みました。
BACK INTO ENGLISH
Walking down the street, I smiled at my mother in the distance.
INTO JAPANESE
通りを歩いていると、遠くにいる母に微笑んだ。
it is unlikely that this phrase will ever reach equilibrium