The poor family having their roadside asado is exaggerated -- for every family there might be doing that, there's another that kicks all of the kids out of the house for the day to go and beg and aren't allowed home until they have some money -- that have school-aged children, but don't send them to be educated because they need the immediate influx of money and can't see that education could provide the longer term escape from their poverty of today. Also that roadside asado scene doesn't exist for the extremely poor here -- think more along the lines of the thousnads of people that rush into the garbage processing plant (CESMA? I can't remember what it's called) at 5pm -- they get 1 - 1.5 hrs to root through the leftovers and get their meals.
I agree with Pericles about the romanticisation (?) of family -- I think a lot of people mistake physical closeness with family members as equating emotional closeness. In fact there are just as many secrets and just as many people harbouring grudges as with any American family. Maybe the dysfunctions are harder to spot at first, but they are definitely there!
And he has it right -- escape from poverty comes with education, but as Pericles point's out you need to provide food and a stable living situation before there's much hope for education. Many families in Argentina only send their children to school because the schools will feed them twice a day. Unfortunately the food they provide is terrible cheap stuff, not sufficient nutrition for a growing child.
The other blow to people at lower income levels are higher rates of cancer, diabetes, heart disease, stroke, HIV, and soaring teen pregnancies. Increased drug use, violence, broken homes etc.
Whereas the rich family in the scenario presented in the initial post have the education and experience that they can change their own situation no matter what happens, the poor in Argentina have little or no power. If you're a single mother here with no education, what are your options for bringing in an income?
Perhaps rather than assume one family is happier than the other in your scenario, it would be better to say the poor family suffer their lot, while the rich family always feels they deserve more, they deserve better.