Analyze the limitations that exist for children of those persons who are incarcerated.
I assume you mean rights such as visitation and access to their incarcerated parent. This is a difficult moral and legal issue. As many prisoners are incarcerated for non-violent offenses, it seems that reasonable contact and access to their family members, especially their children, is something that should be allowed in law and practice.
However, prisons are not normal places and often times, prisoners are not normal people. Society in general and prison officials specifically have an obligation to maintain some control over what moves into the prison, and family members have often been used to smuggle illicit materials to their prisoner relatives. Children are sometimes used because they are least suspected or interfered with.
It seems to me a more nuanced policy of allowing more and easier access to family at the lower levels of security would be wise and practical, while evaluating access to prisoners in maximum security could be handled on a case-by-case basis would be the best option.