It took me a while, but i finally got it working.
I replaced line 325
However, due to the nature of the free version of the ad plugin it’s not possible to get it to align right in an easy matter, but that can be solved by placing the ads inside a table. So i actually had to add two more lines to the code, ending with with the following three lines instead of the one i removed.
echo "<table class=float-right><tr><td>"; echo do_shortcode("$supernews_header_main_google_ads"); echo "</td></tr></table>";
Doing it the way i do now makes it possible to use the admin ui to change the shortcode should the need for it arise.
Oh, and of course i copied the header.php file and placed in my child-theme.