What am I missing? They leave as soon as the child is born? If the mothers take the babies back to Russia, what is accomplished?
Their kid would acquire birthright citizenship in Argentina.
The kids are Argentinian citizens.
They only can become Russian citizens if they apply for Russian citizenship.
The kid can go to Russia, and never apply for or become a Russian citizen.
Of course, Russia could do the kid a big favor and deport them to Argentina.
The kids get an Argentine passport.
Which may eventually be useful for getting the whole family out, if it comes to that.