Hi,
I found the soloution - i think

I took from modules/mod_image_show_gk4/styles/gk_esport/model.php in eSport template from line 67 to line 112 (both included) and replaced the same lines in modules/mod_image_show_gk4/styles/gk_music/model.php in the music template.with these.
As far as i can see, the difference are the line 69 and line 84 - correct me if i am wrong. Now i can unpublish K2 module in right_bottom on the music template

The code from gk_esport are this:
function getDataK2($ids) {
//
require_once (JPATH_SITE.DS.'components'.DS.'com_k2'.DS.'helpers'.DS.'route.php');
// prepare an array
$results = array();
// prepare an query part
$query_ids = implode(',', $ids);
// generate the query
$database = JFactory::getDBO();
// SQL query for slides
$query = '
SELECT
`c`.`id` AS `id`,
`c`.`catid` AS `cid`,
`c`.`title` AS `title`,
`c`.`introtext` AS `introtext`,
`c`.alias AS `alias`,
`c`.`publish_up` AS `date`,
`cats`.alias AS `cat_alias`
FROM
#__k2_items AS `c`
LEFT JOIN
#__k2_categories AS `cats`
ON cats.id = `c`.`id`
WHERE
`c`.`id` IN ('.$query_ids.')
;';
// running query
$database->setQuery($query);
// if results exists
if( $datas = $database->loadObjectList() ) {
// parsing data
foreach($datas as $item) {
// array with prepared image
$results[$item->id] = array(
'id' => $item->id,
'cid' => $item->cid,
'title' => stripslashes($item->title),
'date' => $item->date,
'link' => urldecode(JRoute::_(K2HelperRoute::getItemRoute($item->id.':'.urlencode($item->alias), $item->cid.':'.urlencode($item->cat_alias))))
);
}
}
// return the results
return $results;
}