Whats wrong with this picture?

Unfortunately, that is unlikely. Child labor, like serf labor, usually locks the economy into a condition where it remains necessary. The child labor increases the family's income to survival level - the kids can never quit and go to school, because their income is always necessary for their own support. That will be just as true of the next generation of kids. As long as child labor is available, the income of the adults will be dragged down by it - capital doesn't pay labor any more than it must, to keep a supply of labor available. You seem to be imagining a situation where the laboring child is accumulating some kind of surplus, that the next generation can use.
This is a poorly performing economy and smacks of central planning. In feudal days it was centrally planned by the aristocracy and in much of the Third World the situation is basically the same. It has been pointed out that the tribal mentality that characterizes much of the Third World is something that the rest of humanity had to transcend in order to build economies that produced a significant surplus. Division of labor and economies of scale only go so far in making a small community more productive. They need to trust and care about other communities and learn to cooperate with them, in order to get more leverage out of division of labor and economies of scale. They also need to envision a better future and not settle fatalistically for what they've always had. In other words, they need to move past tribalism and become a true nation, not just a random area defined by lines drawn on a map by colonial administrators.
As far as who is to blame: The first world is to blame for its own actions and behaviors in third world countries. Beyond that, it's a local problem. That is severe blame, btw, incurred by First World countries. They are and have been behaving abominably.
Yes, and they've been doing it since the days of Sumer and the other First Cities--even the Olmecs and Incas. It is the nature of people who have advanced out of the Neolithic Era and built cities to look down on those who have not. Over the past few centuries a growing number of us have learned enough history, anthropology and psychology to realize the unfairness of that attitude (luck plays a colossal role in the transition out of the Stone Age) and also to value the motifs and artifacts of the cultures that lag behind.

That makes us better than our ancestors and we can stop flagellating ourselves by assuming their guilt. We need to look forward and figure out what we can do to make it better. I don't think setting up the Third World as a modern Indian Reservation and "protecting" them from our influence is a viable alternative. Especially since we've already let a couple of really powerful genies out of their bottles like modern medicine and electronic communication which have, respectively, caused a grievous population problem and let them all see how we live.

There is no practical future for these folks--the "Bottom Billion" as they have been recently named--other than joining the other five billion of us in the world community. We can talk all we want about their own responsibility for their fate, the weaknesses in our own cultural patterns, the unfairness of assimilation, etc. But in the end it is we who see the problem most clearly and we who have most of the tools, capital, knowledge and power to fix it.

I don't think we can stand by watching them wallow in misery as we become ever more prosperous and say, "Those poor bastards, if only they could get their act together." Even if we could, would any of us except Max really want to?
"Where does India get the children laborers from?"

children of poor laborers, prostitutes, farmers whose crops have failed, beggars and urchins.

And doesn't the government of India do anything to protect them? Nothing at all? And do you do anything to help them, Sam?

Sam, you complain a lot about the USA, yet your own nation stands by and lets the little Indian kids work in such sweatshops?

Oops, wait .....you have a way of blaming the USA and Americans for that, too, right? If Americans didn't buy the cheap goods, then the little kids wouldn't have to work, right? But, wait, if we didn't buy the goods, then the little kids wouldn't be making any money at all ......so then they'd starve, right? So .....is it better to starve or to work for meager wages?

Baron Max