Well, as I stated, my 2.000 USD figure is just to live in the city without extras (car, trips, plane tickets) and after you pay your taxes (with two kids you might get significant deductions). So yes, the gross income including vacations, RT tickets to Costa Rica and taxes should rather be 3.500 at minimum.
With 5.000 you can enjoy a very comfortable life but it really depends how you spend.
The rule of thumb here is that what you pay 100 you may also pay it 10.
Depends too if you cook by yourself or not : example, if you buy a tiny portion of tiramisu at Franco-Parma (famous delicatessen stores here) it will cost you 12 pesos, while you can buy 1 kilo of mascarpone for 35 pesos, 10 eggs for 3 pesos (I buy 36 eggs for 8 pesos), sugar and 4 pesos of vanillas and I have a 1.5 kilo tiramisu. Bon appétit !
Bilingual schools can be expensive (although you have babies so you don't need to pay for that yet) but for instance, french citizens can send their kids to the french bilingual highschool for free (that's quite new in fact), so depending on your nationality you may find good deals for highschool.
I now live near Pilar in a barrio cerrado, big house, two floors, 2.400 sq meters of garden (20.000 sq ft), 10x5 meters pool (30x15 ft) and I pay 2.000 pesos + 430 pesos expensas. It's a house that could rent too for 2500/3000 but since I have no garantia I offered to pay 1 year in advance and by doing so I explained that the LL would gain because of inflation so they lowered the rent by 20%.
As for the question about if it's cheaper to live outside BS As : Well, the only viable option (middle class life) are the northern suburbs but it is either quite expensive (Vicente Lopez, etc...) or you may find lower rates (Florida, ...) but the barrios are a bit more insecure.
I would not buy a car here, taxis are quite cheap and if needed, better rent a new one once in a while.
Internet is quite expensive, true but my own solution is to use a tethered iphone : I get unlimited internet + cell phone for 229 pesos a month. Bandwith is like a half mega but I still can watch live TV.
Anyway the first year, be ready to pay a bit more for everything until you settle and know better how to spend wisely.