YOU SAID:
me and my mom went on a walk
INTO JAPANESE
私と私の母は散歩に行きました
BACK INTO ENGLISH
I and my mother went for a walk
INTO JAPANESE
私と母は散歩に出かけました
BACK INTO ENGLISH
My mother and I went for a walk
INTO JAPANESE
母と私は散歩に行きました
BACK INTO ENGLISH
Mother and I went for a walk
INTO JAPANESE
母と私は散歩に行きました
BACK INTO ENGLISH
Mother and I went for a walk
That didn't even make that much sense in English.