Enabling modules in an update hook.

mymodule.install

/**
 * Enable modules.
 * Normally we'd use master module for this but sometimes you can't run anything other than updb in production.
 */
function mymodule_update_7001(&$sandbox) {

  $modules = array(
    'mymodule_one',
    'mymodule_two',
    'mymodule_three',
  );

  if (!isset($sandbox['progress'])) {
    $sandbox['progress'] = 0;
    $sandbox['max'] = count($modules);
  }

  $module = $modules[$sandbox['progress']];
  module_enable(array($module));
  drupal_flush_all_caches();

  $sandbox['progress']++;
  $sandbox['#finished'] = $sandbox['progress'] / $sandbox['max'];
}