Add home link to start or end of menu From http://wordpress.stackexchange.com/questions/121309/how-do-i-programatically-insert-a-new-menu-item

add_custom_link

// Filter wp_nav_menu() to add additional links and other output
function new_nav_menu_items($items) {
    $homelink = '<li class="home"><a href="' . home_url( '/' ) . '">' . __('Home') . '</a></li>';
    // add the home link to the end of the menu
    $items = $items . $homelink;
    return $items;
}
add_filter( 'wp_nav_menu_items', 'new_nav_menu_items' );

or add_filter( 'wp_nav_menu_{$menu->slug}_items', 'new_nav_menu_items' );
e.g. add_filter( 'wp_nav_menu_primary-navigation_items', 'new_nav_menu_items' );