I want to detect the insertion of a new div element only as a direct child of the parent div.
Example:
Use DOMNodeInserted on the parent and check the event.target.parentNode of the added element. If its id is parent, then the element is a direct descendant.
Demo: http://jsfiddle.net/ThinkingStiff/f2w7V/
document.getElementById( 'parent' ).addEventListener( 'DOMNodeInserted', function ( event ) {
if( event.target.parentNode.id == 'parent' ) {
//direct descendant
};
}, false );