[Theme: Twenty Eleven] Menu issue with twenty eleven child theme

Try using Firefox with the Firebug add-on for this kind of CSS work.
http://getfirebug.com/

When I add a custom menu

The home menu item is set in functions.php so you can remove the menu item by removing the filter and then use a URL menu item to point to the home page.

From Twenty Eleven functions.php

/**
 * Get our wp_nav_menu() fallback, wp_page_menu(), to show a home link.
 */
function twentyeleven_page_menu_args( $args ) {
	$args['show_home'] = true;
	return $args;
}
add_filter( 'wp_page_menu_args', 'twentyeleven_page_menu_args' );

Assuming you using the custom menu css-classes?

If so then in the child themes function.php

/** START function will remove the parent filter  */
add_action( 'after_setup_theme', 'child_remove_filters' );
if ( !function_exists( 'child_remove_filters' ) ):
function child_remove_filters() {
	remove_filter( 'wp_page_menu_args', 'twentyeleven_page_menu_args' );
}
endif;
/** END function will remove the parent filter  */

Now create a URL menu item with a link to the home page, and add the Menu Item css-class

HTH

David