What problems might researchers face in carrying out studies that involve changing of the residential environment of deprived children
There is a potential for resentment on the part of the individuals involved in the study. Resentment might come from parents, especially if children are removed from their parents. There might also be resentment among those left behind. Finally, resentment in the children themselves can result as children are removed from everything they have known. Even if the conditions the child lived in before were terrible, the child will still prefer the comfort of what is known to the isolation of the new environment. No matter how bad things were, that was home.
As pohnpei pointed out, there are ethical considerations to be considered, as bringing harm or delaying help to a subject would be unethical. However, another problem would be your inability to control the variables. Sure you remove the child to a different environment. Would this mean changing schools, because you would then have other elements that changed--not just the environment.
I can see at least two problems that would be faced by a researcher who wanted to carry out such a study.
The first involves the need to treat human subjects ethically. A researcher could not simply take children away from their families and put them in a different home environment. This would never be allowed in the modern world.
Second, a researcher might try to get around this by moving the whole family to better living quarters. This would negate the problem of taking kids away from their families. But now you run in to the problem of a confounding variable. You have brought along this entire family who are also having to react to changing circumstances. Their reactions may affect that of your research subject. In other words, if something happens with the child you are studying (a change in the dependent variable) will you know if it was changed by the change in environment (the independent variable) or by the family's reaction to that change (a confounding variable)?