We will be in a similar situation soon and I want to ensure we are following the requirements.
Dad is US citizen only. Mom is Argentine but naturalized US citizen. Travels on US passport but brings Argentine one in case. Kid is US citizen only with US passport. Just to be safe we are bringing an apostilled birth and marriage certificate. Having done some research, we will not be getting him his DNI or citizenship. When he is 18 and if he wants to pursue it, the option appears open. For now, living in the US it will create unnecessary chaos and additional requirements for him whenever he visits Argentina as a child if he is deemed Argentine in addition to a US citizen.
My question is: for domestic travel within Argentina, are there any requirements for documentation? I.e. if he is traveling alone with mom and they are ever stopped by gendarmes or something. Does it make sense to get the escribano letter etc. giving permission to travel domestically for times I am not with them (seems like it would not as law only applies to international travel and you have to specify destination country). I just don't want to run into any problems.
Just to follow-up to my concern above, the border agents did NOT request anything but our son's Passport when we crossed the border. If we were travelling internally, I would imagine all they would ask for would be the passport to check that his tourist stamp is still valid.
Not sure about travelling internally with just one parent, but very much doubt it would be necessary to have the escribano note if not crossing a border!
NOTE: even though your wife is a naturilzed US Citizen, she would need to enter/leave on her DNI or Argentine Passport to Argentina - there is no other choice!