http://sqlfiddle.com/#!2/808cc/1 - See for Schema and Query

The query returns the expected results, I want to see all the child_ids that match all the criteria in the IN() function. If I didn't use HAVING COUNT then there query would return results that meet any of the id's in the IN function.

Is there a cleaner way of doing this? What I have at the min seems more like a hack.