my family

my family is not big
my family is I , my mom and my dog
grandmom & granddad leave not with us

Capitalize words at the beginning of sentences, like "My family is not big."

It may be better to say, "I have a small family" (У меня есть маленькая семья.) instead of "My family is not big" (Моя семья небольшая).

Instead of "My family is I, my mom, and my dog" (Моя семья - Я, моя мама и моя собака)  try "In my family there is my mom, my dog, and I" (В моей семье есть моя мама, моя собака и я.). When listing in English (my mom, my dog and I) "I" almost always comes last in the order.

The last sentence should look like "Grandmother and grandfather (you can always say Grandmom and Granddad if you like) do not live with us" (Они не живут с нами) instead of "leave not with us"