I have searched this thread from the beginning and I can't find a single post or even indirect statement asserting that couples may not live together in Vietnam without being legally married. I remain confused why people keep asserting that in such a strident tone, as if someone was contradicting them. No one is disputing that fact.
Perhaps those who are so adamant about the matter are missing the point that the OP wishes to have his prospective wife and her children emigrate to the US. To do that they must be married. This is not Vietnamese law. It is US immigration law. Vietnamese laws on cohabitation are irrelevant to his questions.