I would like to structure my title tags to display: Site Name | Page Title
According to the codex this should work:
<?php wp_title('|',true,'right'); ?><?php bloginfo('name'); ?>
but it is rendering in reverse: Page Title | Site Name
Any other location where this is controlled, that may be causing an override?
According to the codex, you can edit the title to do exactly what you are wanting to do.
<title><?php is_home() ? bloginfo('description') : wp_title('', false); ?> | <?php bloginfo('name'); ?></title>
Is that what you were looking for?