This Droplet will make it simple to add a YouTube video to a page.
Just copy the youtube ID of the video and add it to the Droplet call. No problems with embedded objects in the WYSIWYG editor.
if (!isset($v) || !$v) return true;
$parm = 'modestbranding=1&rel=0&showinfo=1&showsearch=0&theme=dark&hd=1&wmode=opaque';
$returnvalue = '<div class="vid">';
$returnvalue .= " <iframe allowfullscreen type='text/html' src='//www.youtube.com/embed/$v?$parm' frameborder='0'></iframe>";
$returnvalue .= '</div>';
return $returnvalue;