YOU SAID:

my dog is sleeping beside my mom

INTO JAPANESE

私の犬は私の母のそばで寝ています

BACK INTO ENGLISH

My dog is asleep by my mother

INTO JAPANESE

私の犬は私の母によって眠っています

BACK INTO ENGLISH

My dog is sleeping with my mother

INTO JAPANESE

私の犬は私の母と一緒に寝ています

BACK INTO ENGLISH

My dog is sleeping with my mother