I think you think this is easier than it is. It’s real difficult to do an international adoption with a live parent. Father is dead? Mother is willing to give up this child?!? If so what’s the purpose of her immigrating here in a few years as well.
WARNING: Vietnam is party to the Hague Adoption Convention. Do not adopt or obtain legal custody of a child in Vietnam before a U.S. consular officer issues an “Article 5/17 Letter” in the case.
Start by reading:
https://travel.state.gov/content/travel/en/Intercountry-Adoption/Intercountry-Adoption-Country-Information/VietNam.html
I would strongly suggest consulting an attorney with experience in foreign adoptions......This is a complicated process......Adoption does not guarantee immigration benefits.