How to alter sort handler to keep existing order intact in views

I created a views page using foo plugin.When a user visit the page the city and Clinic/Hospital columns by default are being rendered alphabetically (ASC) as in below screenshot.

EDIT: Let’s say for example. City is Bangalore and only for Bangalore Clinic/Hospital(C/H) column is alphabetically ordered(say Hospitals A,B,C,D…).Then user clicks on City head,then for Bangalore C/H column is alphabetically disordered(ex B,D,C,H…) but records are still correct to Bangalore city means those clinic/hospitals are located in Bangalore .Same goes for other cities too.What I want is C/H col should be ordered as earlier (alphabetical) City by City but no matter how city is ordered.

When user clicks on City head (which is sortable),the order of Clinic/Hospital goes heywire (no more alphabetical order) like below image:

Problem: How can I make my Clinic/Hospital order intact even after user clicks on City head.

Below is my views configuration:

I am using Drupal 7.41 and views 3.0

Tried so far:

function mymodule_views_query_alter(&$view, &$query) {
   if($view->name == 'list_of_doctors' && $view->current_display == 'page_1' && count($query->orderby) == 1)
    {

        $query->orderby[1] = array(
             'field' => 'field_data_field_clinic_hospital_field_clinic_hospital_value',
             'direction' => 'ASC',
            );
    }
 }

}

But after clicking City head,whole table vanishes.

/**
 * Implements hook_views_query_alter().
 */
function YOUR_MODULE_NAME_views_query_alter(&$view, &$query) {
  if ($view->name === 'YOUR_VIEWS_NAME' && $view->current_display === 'YOUR_VIEWS_DISPLAY_NAME' && count($query->orderby) == 1) {
    $query->orderby[1] = array(
      'field' => 'YOUR_SECONDARY_SORT_FIELD',
      'direction' => 'ASC',
    );
  }
}