I heavily expect that you are NOT writing your OOP very well if this is the case. It seems that you should extend your child NOT your parent in order to use those methods.
You CANNOT use a method of a child that has not been instantiated UNLESS that method is static. In your case :
$blah = new action_parent();
child does NOT exist yet because you don't have an instance and have extended from the parent class.
Please provide the PHP code for what you are trying to do/extend.