Argentine passports

Since we're planning to travel, I've been trying to get some of the basics in order. Number one item on the list: passports for everyone. Julian's is expired. Mine is expired. Enzo's never had one.To renew Julian's we'll have to make a trip to the Argentine consulate in Houston. I also discovered that I could get an Argentine passport since I'm the spouse of an Argentine citizen. Here's where I found all the information on Argentine passports and what's required.Does anyone know if I'd be able to just get an Argentine passport and not have to get a new US passport? If I plan to come back to the US will I need to enter with a US passport?This is getting more complicated than I initially thought it would be.