there's no way Hanoi is any better than any village in the middle of nowhere. Thailand is much better than Vietnam, even though I like it there. In Thailand the variety of products, attitude of people, and things to do are greater
And honestly Hanoi is just boring, full of rude people, and dirty. IMO only Da Nang, Sapa, Hoi An, Hue are worth visiting. More corruption there as well and although the Vietnamese are really friendly, many A-holes too, always trying to get the upper hand on you and they don't know personal space and manners
Brazilians don't need visa to Schengen countries up to 90 days but your point is valid, since she's a Italian citizen it's best to check-in with her Italian passport. Also, as you said the data on the immigration database will the the one corresponding to the Brazilian passport