You need to use xPDOQuery to fetch them, the published status is no use with the getChildIds directly:
$cids = $modx->getChildIds($root, 6, array('context' => 'web'));
$crit = $modx->newQuery('modResource');
$crit->select($modx->getSelectColumns('modResource', '', '', array('id')));
$crit->where(array('id:IN' => $cids, 'published' => 1));
$collection = $modx->getCollection('modResource', $crit);
$ids = array();
foreach($collection as $resource) {
$ids[] = $resource->get('id');
}
$ids will contain the id's of children with publish status 1. Hopefully there ain't many typos as I wrote this directly to reply field