Trying to create a widget that submits a form and takes you to another search page
It's not clear from your question, so I will assume that you are missing the following:

/**
 * Submit handler for facet form.
 */
function resource_library_facetapi_select_submit($form, &amp;$form_state) {
  $form_state['redirect'] = array(
    $_GET['q'],
    array('query' =&gt; unserialize($form_state['values']['select'])),
  );
}