Moving the logo and text/play button independently would be difficult but there is an alternative. Remove the logo from the settings field in your homepage, and instead add it manually into headlines.php. That way you have total control and you're not fighting against the existing CSS.
So in headlines.php in your child theme you can add something like this at the very start of the file:
And then in Custom CSS all you need is this:
<img class="headline-logo" src="http://dopamine.it/wp-content/uploads/2014/01/logo-dopamine.tv_.png" alt="YOUR ALT TEXT">
margin: 20px 0 0 20px;