Anthem

I think they do this so they do not look up to anyone but them. With a parent the kids may look up to the parents more than the dictator. therefor they take the children from their parents.
They would enforce this because they wouldn't want the children to learn their parents view of the situation. The parents could make it so their kids would want to revolt after knowing what a terrible situation it is to be in
I believe that dictatorial leaders enforce children living apart from their families because they want the kids to be emotionally separated from their parents or family. They want them to focus on other things such as a job or power. They might also do this to present stricter discipline and make sure the job of raising a child gets done the way they think it should be done. They might think that if they stayed with their parents the parents would have an emotional attachment and may not do the job that needs to be done. They want control over everything as most dictatorial leaders do. That's why I think they enforce the living arrangements.
Leaders enforce this because it eliminates the passing of knowledge from generation to generation. It also helps to keep peace because if someone doesn't know their child they have no reason to fight for something. If they know their children they have a reason to fight for something they are willing to destroy the dictatorship because they want what is best for their children. They are willing to sacrifice themselves because they love their children. This is another reason for the separation, love. If the parents never meet their children they can't love them and love leads to many things that could hurt the dictatorship. Passing of knowledge helps stories and truths to be passed because you can learn from past experiences and thus us them to better their lives. This may lead to a revolution against the government. These are the reasons that a dictatorial government would separate children from their parents.