Also one thing to keep in mind is that in Argentina inflation can get out of control pretty quickly. You saw you want to come down for a few years. Well, I think everyone on this board would agree with me that any budget that would have been given for 3 years ago is pretty much entirely irrelevant today. In the past six months alone the dollar has gone up from 3.09:1 to 3.62:1, but inflation has been going up at around 20-25% on many goods (and more on many others!)
Here's the same advice I always give, come down, try it for 6 months, see what you think. If that's not an option (which probably isn't since you've got kids), then come down for a month.
Also you don't mention anything about your kids and what you'd want for them here -- are they in at all school yet? do you want them at a private school? are they in university? School starts very young here -- 3 years old and a lot of places take them younger. Private schools can run pretty high, and a lot of them are in the Northern Zone, which is an entirely different lifestyle than BA. You would need a car. There's a LOT more that you need to research before anyone can stat giving you numbers. Have you visited BA before? It's not the cheap paradise that the papers claim, and a lot of people end up deciding it's not for them.
I think rather than figuring out how much it costs to live, you'd be better off figuring out how you can make a 1-6 month stay happen first.