So far, the only solution I come from is to do like this :
In my sub controller, I should always have id_other_model in the url, so I added this method :
public function initProcess() {
parent::initProcess();
self::$currentIndex .= '&id_other_model='.(int)Tools::getValue('id_other_model');
}
And so far it works well.
If there is a better alternative, I'd appreciate to know it :)