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Tell your wife to find someone who has connections in the Phong Ho Tich, of your So Tu Phap, and get them to assist you.  Which ever "high power" attorney you find will do the same thing, for a crazy fee, of course.  If she thinks hard enough, I am certain that she can think of someone, or somebody who will know someone there.  That is how such problems are resolved here.

As Wild 1 stated, connections are the best way to get things done quickly.
Ask around, I'm sure a friend of a friends cousin's sister inlaw will know someone.
Hope u get it sorted out soon

Yeah.  No lawyer knows more about the laws than the guys who make and enforce them, as they go along.  Get to know one well enough, he can make you a few laws.  But you should let your Vietnamese families or friends do it.  These folks will not cooperate with foreigners!!!

An unconnected attorney can make the case a lot harder for you.  Ho Chi Minh, the man on all Vietnamese bills, is the best attorney here.  Let him represent you.

I think you need:  1. hospital birth record( original)     2. agreement on child^s nationality  3. marriage certificate  4. indentity card or passport( you and your wife-copy)  5. household registrationbook or resident card or temporary resident card.          After that, you come Department of Justice ,141-143 Pasteur, district 3.   Good luck.