со своим сыном

with his/her own son, with his own son

→ со
phrase Rare #48,876
with his/her own son The possessive свой refers to the subject of the sentence, so the exact English form depends on the subject: with my own son, with your own son, with his own son, and so on.
RU: Она часто гуляет со своим сыном.
EN: She often goes for walks with her son.

В Кёнигсберге жила одна вдова со своим сыном.

A widow and her son lived in Königsberg.

— Жертвоприношение (1986)

Я не могу всё послать и тусить со своим сыном!

I can't just tell everyone to fuck off and hang out with my son!

— Мамочка (2014)

Сэл, если ты не против, я хочу побыть со своим сыном.

Sal, if you don't mind, I'd like to spend some time with my son.

— Делай как надо (1989)

phrase Rare #48,877
with his own son Uses the reflexive possessive "своим" to show the son belongs to the subject of the sentence.
RU: Маша гуляет со своим сыном в парке.
EN: Masha is walking with her own son in the park.

Потанцуй со своим сыном!

Dance with your son!

— Мамочка (2014)

Я пошла со своим сыном.

I went with my son.

— Всё о моей матери (1999)

Я говорю со своим сыном.

I'm talking to my son.

— Пожары (2010)

Том играет со своим сыном.

Tom is playing with his son.