Actually, LH, historically Vietnam was two countries, with the north (Tonkin), under the Trinhs, tied fairly closely with China and the south (Cochin), under the Nguyens, more connected to the other regions of SE Asia and the archipelago. The latter managed to consolidate the entire "nation" under its rule for about 40 years, in the late 18th century, until it was, in turn, taken by the French.

Otherwise, except for the usual political and grammatical spin, your history is essentially correct.