The mini login form can either have the popup appear below and to the left or right. When creating the form, call $form->setMiniLoginFormPopupPosition(), with the first arg being either 'left' or 'right'. This is actually the 'arrow' position, so it's the opposite of what you expect (in other words, if you set it to 'left', the box will extend out to the right under the mini login form.
Signature
public function setMiniLoginFormPopupPosition(
$dir )