Just want to give an update. We decided to stay in Argentina for all 3 nights. Taxi from IGU to Puerto was easy, and the fare was 90 Reais, which we accepted. (Various searches suggest going rate between 85 to 100 Reais). Taxi driver took our passport inside Brazilian border control to have it stamped, and on the Argentinian side, all our passports stamped at the booth.

Coming back, we decided to ask the hotel to arrange a car. Fare was 450 Pesos, which was a bit steep (as I have seen some posting on the walls in Puerto advertising 250-300 Pesos), but we decided to just let the hotel do it. Again, driver took our passports inside the Brazilian office for stamping (and he filled the entry cards for us as well).

We took it easy at the Argentinian side, and spent both days there. As the park offers 50% off 2nd day. Lots of trails, and the boat ride kept us occupied.

The money issue was interesting in Puerto. I can post more if someone's interested to know.