My wife, son and I currently live in Lima, Peru. We're planning on taking a trip to Poland in June/July sometime. My son is an American/Peruvian dual citizen.
We recently traveled to Chile, and when going through the airport I stupidly showed the person checking identifications my son's American passport, instead of his Peruvian passport. When this happened, the airport employee told us we would need to pay for the x amount of days my son has been in Peru (he was born in Peru, and has never left to any other country outside of South America). Because apparently he has overstayed his Tourist Visa. So instead we showed him his Peruvian passport, and all was well. If we tried leaving on his American passport we would need to have paid a few hundred dollars in penalties.
Now, the issue or the question that comes up for us is will my son be able to leave Peru on his Peruvian passport in order to go to Poland? Once we arrive in Poland, we would just use his American passport? In Chile it was different because we could leave and arrive both on his Peruvian passport without a problem, as Peruvians can travel without restrictions to Chile. Peruvians traveling to Poland require a Visa.