Thankful to the Lord, I found a solution for anyone else that comes across this issue. I took this function from the WordPress codex and modified it to soot my needs
function get_menu($menu_name) {
$menu_items = wp_get_nav_menu_items($menu_name);
$menu_list="";
$count = 0;
$submenu = false;
foreach( $menu_items as $menu_item ) {
$link = $menu_item->url;
$title = $menu_item->title;
if ( !$menu_item->menu_item_parent ) {
$parent_id = $menu_item->ID;
if(!empty($menu_items[$count + 1]) && $menu_items[ $count + 1 ]->menu_item_parent == $parent_id ) { //Checking for child
$menu_list .= '<li class="menu-item menu-item-has-children"><a href="'.$link.'">'.$title.'</a>';
}else{
$menu_list .= '<li class="menu-item"><a href="'.$link.'">'.$title.'</a>';
}
}
if ( $parent_id == $menu_item->menu_item_parent ) {
if ( !$submenu ) {
$submenu = true;
$menu_list .= '<ul class="sub-menu">';
}
$menu_list .= '<li class="menu-item"><a href="'.$link.'">'.$title.'</a></li>';
if(empty($menu_items[$count + 1]) || $menu_items[ $count + 1 ]->menu_item_parent != $parent_id && $submenu) {
$menu_list .= '</ul>';
$submenu = false;
}
}
if (empty($menu_items[$count + 1]) || $menu_items[ $count + 1 ]->menu_item_parent != $parent_id ) {
$menu_list .= '</li>';
$submenu = false;
}
$count++;
}
return $menu_list;
}
I then called the function from my menu filter (see function above) like this.
if( 'main-menu' === $args -> menu ) {
$items .= $fcs_menu = get_menu('SECOND MENU NAME GOES HERE');
$items .= '<li class="menu-item company-info">'.do_shortcode('[show-company-info]').'</li>';
$items .= '<li class="menu-item social-networks">'.$social_icons.'</li>';
}