After looking through the Profile2 Git repository viewer for v1.3. I believe you want to do something like the following using profile2_attach_form. The `profile2_attach_form has the following API comment and function signature:
/**
* Attaches the profile forms of the profiles set in
* $form_state['profiles'].
*
* Modules may alter the profile2 entity form regardless to which form it is
* attached by making use of hook_form_profile2_form_alter().
*
* @param $form
* The form to which to attach the profile2 form. For each profile the form
* is added to @code $form['profile_' . $profile->type] @endcode. This helper
* also adds in a validation and a submit handler caring for the attached
* profile forms.
*
* @see hook_form_profile2_form_alter()
* @see profile2_form_validate_handler()
* @see profile2_form_submit_handler()
*/
function profile2_attach_form(&$form, &$form_state) { /* ... */ }
So, you could use it as follows by slightly modifying your code:
$user_register_form = drupal_get_form('user_register_form');
$form_state['profiles'] = array(
'CUSTOM_PROFILE_TYPE_NAME' => profile2_get_types('CUSTOM_PROFILE_TYPE_NAME')
);
profile2_attach_form($user_register_form, $form_state);
print(drupal_render($user_register_form));
If you need to tweak any profile entity form displayed in some of your registration page(s), you may want to implement the specific FORM_ID version of hook_form alter, hook_form_profile2_form_alter()
.
EDIT 01/15/2015
minor API clarification and code cleanup from comments.