Baby joy for travelling couple who spent pandemic stranded in Mendoza

They are very confused. There is nothing rare about dual or triple citizenship in Argentina.
Second, the citizenship of the baby cannot be rennounce and for they it makew no sense a PR because they have to come here every 2 years.
The issues they had were for lack of proper legal advice because the baby does not need more evidence of her atatus than the birth certificate of the parents, because the passports are not good enough for that.
Because of the lack proper legal advice, they do not know about the Principle of Unification of The Familly Nationality that for sure works in Argentina and the UK but not in the Us whose law is more primitive. The UK has a long tradition on Roman Citizenship Law, copied by Argentina while the US since the 1920’ abandoned it for martial medieval law.