There is a detailed examination of the legal issues in Camreta v. Greene, from Diane Redleaf, Executive Director of the Family Defense Center. FDC co-ordinated the national amicus effort in support of the Greene family and full Fourth Amendment rights for children. She wrote this analysis for the American Bar Association Section of Litigation.
In addition, the "friend of the court" brief from the Center for Individual Rights offers a particularly clear explanation of the legal issues in this case, including the question of whether it should be before the Supreme Court at all.
See also this excellent analysis from Prof. Mark Brown of Capital University Law School. Prof. Brown also wrote this amicus brief.