The second one is MUCH better. It really gives an insight into your life. Is your essay to describe & write about how meaningful it is to you supposed to be the same place?
My most favorite place has always been my mother's house.
I'm assuming this is in your native country Vietnam? Specify this, as you live in the US.
and her four months pregnancy of me
,four months pregnant with me.
place I would have to go almost every summer
have to go? sounds like you didn't really want to. Leaving out the word 'have' would sound better
My father was a lieutenant. He was forced to leave the country (where did he go to? the USA?) when the Communist took over the South of Vietnam
My father was a lieutenant in the Vietnamese(?) army and was forced to leave Vietnam when the Communists took over.
he could come back nor reunite with us. Therefore, he has remarried. However, life is changing.
he would never be able to reunite with us so he remarried. However things changed
My father could be able to come back when I was twelve. Unfortunately, my father could not sponsor my mother to the United States as of his legal wife, but me. I was sponsored to America and separated from my mother since then.
My father was able to come back (from where?) when I was twelve (explain here he wanted to bring you over to the US) but unfortunately he could only sponsor me because my mother was not his legal wife. I moved to the United States and have only seen my mother during the summers since then (I changed that sentence because your essay is about how you visited her every summer)