See my Book: Learning from My Mother's Voice: Family Legend and the Chinese American Immigration Experience. Can you develop your family legend by sharing your narrative as a tool to heal and bond among immigrant families?
Your question is one I posed to myself and attempt to answer in fiction several stories. Although not an immigrant family, my family lived in an overwhelmingly immigrant steel mill town. The idea of two worlds must play a role in the rifts in families. The grimness of the industrial or urban surroundings etches some hard positions in families.
I am editing a book called Children of Steel that is comprised of the fiction short stories of people who have grown up in or who have lived in steel mill towns. There are many codes of silence in coming from what is perceived as a "lesser" background. Immigrants feel this at times. Sometimes just giving people permission to even have a story to tell no matter what "take" they have on it makes them breathe easier. I do this every time I send out to the group, tell them that story is their own and nobody else can tell it.
One other resource is the text The Elephant in the Room: Silence and Denial in Daily Life by Eviatar Zerubavel.
Yes...telling a story, your story gives you a voice, it is a humanizing element. It even moves the individual to higher cognition of events and own emotions and reduces stress. Telling your story moves personal events from narrow alleyways towards a social expression of experiences and thereby addresses issues of isolation, alienation etc