Retrieve parent and child data using child id
I was able to figure out what I wanted to achieve.

I just added an OR on right join. (http://sqlfiddle.com/#!9/f9f1c6/12)

Select parent.child_id, parent.parent_id, parent.child_name from Child c
RIGHT JOIN (
  Select NULL as child_id, parent.id as parent_id, parent_name as child_name 
  from parent
  Union
  Select child.id as child_id, NULL as parent_id, child_name 
  from Child
) parent on parent.parent_id = c.parent_id OR parent.child_id = c.id
WHERE c.id = '2';