I get what the OP is talking about. I have family members who came to this country as Cambodian refugees so I'll speak to this. I AGREE about speaking English. My family members learned English. They went to our schools without translators, they assimilated. They even became proud American citizens.
However, in no way did they lose their own heritage. They still speak their language, eat their traditional foods, etc. They were shocked when they moved into communities with larger immigrant populations. They discovered that while they had the "best of both worlds", many of their new friends had limited social circles, limited work opportunities, limited educational opportunities.... and they were thankful that they had immigrated to an area where they were sort of forced to assimilate.
When our family members first came, by law they were offered translators at school, welfare. etc. Together we decided to turn it all down and work at helping them become independent of that kind of help as quickly as possible. While it was not the easiest option (they were a family of 10), they are now of family of highly educated, highly successful Cambodian Americans.
Learning to get along in the society in which you are living does not mean you have to give up your own heritage. There are ex-patriots living all over the world that could tell you that.