Hi,
This problem has been fixed with the new version. If the shopping cart page opens with mobile device, the pages open as a standalone page, instead of modal popup. But looks like you have the old version. But there is a simple patch for your case too.
Basically you need to increase the "HEIGHT" of those modal popup window to display the whole fields . So the scrolling won't be necessary (within the popup modal).
Check this topic to see how to increase the "HEIGHT" value of those modal popup windows:
www.flexiblewebdesign.com/forum-joomla-virtuemart-template-darkmart-support/1478-pop-up-size#6974
FYI: The PHP you need to make modification is this:
/templates/YOUR_TEMPLATE/html/com_virtuemart/user/login.php
Regards
Support