While my kids are older, I have friends who moved to Buenos Aires with three young children.
they did fine. The kids were just a bit older, more like 5-10 years of age, so they all went directly into regular public schools, and thrived.
They did, indeed, buy a minivan- a Citroen Picasso
http://en.wikipedia.org/wiki/Citroën_C4_Picasso
I rode in in it several times, its a bit smaller than current american minivans, but pretty similar to my old first generation Honda Odyssey, or the very earliest Chrysler minivans, in size.
Driving in Buenos Aires is not easy- I would say its comparable to driving in Paris or NYC or Rome, all of which I have driven in, as opposed to LA or Seattle.
But its totally do-able, and I have many friends who do it every day.
Domestic help is cheap, and pretty much everybody with kids has it.
As for houses versus apartments, its about how you want to live- one of the great things about buenos aires is that its a real city- and, to take advantage of all that it offers, you would live IN it, not 30 or 40 minutes away in a house in the suburbs. Like living in Manhattan, as opposed to Great Neck or New Jersey. Only you know which you prefer.
There are houses in some neighborhoods, usually denser than you would find in the USA, but they tend to be farther from the center, and more expensive. I have friends who live in houses in Caballito, but the houses that are left are not cheap. In the northern suburbs, past the city limit, in places like Martinez, or Olivos or San Isidro, there are houses with yards, but you are a long drive or train ride from all the action.
My friends with the young kids lived right in Palermo Soho, their kids could walk to a corner store, or even to school.
You see kids everywhere, every day, at virtually every hour of the day. Everyone here loves kids, and they are welcome almost everywhere. I have been taking the bus home from a concert, at two in the morning, on a hot summer night, and the sidewalk cafes will still have families with young (under 5) kids playing at that hour. You see unattended kids grade school age an up, walking, taking buses, and the subway, every day.
Your kids will have a great time.
If it was me, I would be looking in or around the belt of parks, which run from Recoleta up towards Belgrano- still urban, easy access to everything, and close in. Palermo Viejo, Las Canitas, Belgrano.