How do I direct users to my custom search?
I would use hook_form_alter() to alter the default search form to call your own submit function.

So, in your custom module do something like this:

// Alter regular search box
function YOURMODULENAME_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  if($form["#id"] == 'search-block-form') {
    // Add any additional fields or things you need here

    ...

    // Modify the submit handler that is called
    $form['#submit'] = array('YOUR_CUSTOM_search_submit');
  }
}


This actually modifies precisely that block search form, so including the search block just like you've described in the template file should work once you've implemented the form alter.