No, you are making my point...
To clairify:
Yesterday's **FIRST WAVE** immigrants thought of their home country as their first country. Hence the Irish Catholic church a block down the street from the Italian Catholic Church. Their children and descendants (you) assimilated much more easily.
Today's **First Wave** immigrants are they same as yesterdays. The still think of the motherland as their real country. Their kids, like the others will think of the US as their country (it is where they were born, and they will feel comfortable here). It is they way it works. I see it with my residents and I am sure of it.
I sure hope you are right.