Argentina is great value when traveling on US dollars, easy for travel in with limited Spanish.
I'd suggest for your first trip concentrate on the areas near the Andes, it's spectacular.
As for teaching the little ones a new language, some basics, then some kids TV shows ,then introduce some music they will latch onto catchy tunes and you can translate, in no time they will get by, and improve daily once you are over there.
Kids are like sponges they suck up new languages fast.
Don't over think it.