Can Parents Get Access to Facebook Accounts of Their Children

Children under 13 year age are not allowed to access Facebook, but In Addition Parents of children 13 years or older can consider whether their child should be supervised during the child's use of Facebook Site.

Q : How can we get access to our child's Facebook ID ?
A: Facebook has generally Forbidden by federal and many states law to give unauthorized access to someone who is not an account holder. Parents may wants to install monitoring software on home computers if they are concerned about what their children are doing online.
If your child age is below 13 and you think he/she has created a Facebook account, however the Children's Online Privacy Protection Act gives you the right to access personal info they have provided before Facebook follows its policy promptly deleting such data. You may get direct access and delete such data by having them sign into the account or deactivating it, or by making a request by email to Facebook Please send request to  privacy@facebook.com with subject line "COPPA Data Request".
Facebook urges parents to talk to their children about the dangers they may encounter online, to make sure they are using Facebook in a safe way. Children must know that they have to report to their Parents and Facebook using the tools made available through sites if he/she saw any inappropriate or offensive Facebook content