Ajax callback of select form field not triggered when changed by javascript, only when changed manually
try to specify the event, like 

$form['children']['number_children'] = array(
  '#title' =&gt; t('Počet detí'),
  '#type' =&gt; 'select',
  '#options' =&gt; range(0, 15),
  '#default_value' =&gt; $number_children,
  '#ajax' =&gt; array(
    'callback' =&gt; 'ajax_callback_registration_children',
    'wrapper' =&gt; 'children-div',
    'method' =&gt; 'replace',
    'effect' =&gt; 'fade',
    'event' =&gt; 'change',
  ),
);


this should be sufficent .. (but select uses change already as default event ..)

other things to try could be

add a custom event, like:

'event' =&gt; 'custom_change',

jQuery('select').trigger('custom_change');


See How to trigger Ajax forms machinery

or invoke the callback yourself:

Drupal.ajax['#ID'].eventResponse('#ID');