// Code in functions.php:

function my_theme_scripts() {
  
  if ( !is_admin() ) { // instruction to only load if it is not the admin area
   // register your script location, dependencies and version
   wp_deregister_script( 'jquery' );
   wp_register_script( 'jquery', 'http://ajax.googleapis.com/ajax/libs/jquery/1.5.1/jquery.min.js');
   wp_enqueue_script( 'jquery' );
   
   wp_register_script('custom_script',
       get_bloginfo('stylesheet_directory') . '/js/expand_collapse.js',
       array('jquery'),
       '1.0' );
   // enqueue the script
   wp_enqueue_script('custom_script');
}
}   
 
add_action('init', 'my_theme_scripts');

// /js/expand_collapse.js in child theme:

<script type="text/javascript">
        jQuery(document).ready(function($) {
            $('#upNav').hide();
			
			$('#showBtn').click(function() {
  				$('#upNav').toggle();
			});
			
			$('#parent').hover(function() {
  				$('#upNav').show();
			});
			
			$('#parentNav').mouseleave(function() {
  				$('#upNav').hide();
			});
        });
        </script>

Enqueue Javascript

PHP