Parents can be restricted from updating the address of their child and/or spouse. But, it is still possible for one parent to update the address for the entire family.
  1. Select Core from the menu in the upper left
  2. Navigate to Security
  3. Profile Access
  4. Profile Relationship Access

This occurs when the family 'shares' an address. If it is updated by one Parent, the relations linked to the shared address will also have their information updated.