Linking Standalone CSS to new page template issues.

Hello fellow WordPress users,

So last night, after slaving away working on a nice sleek stylesheet for a created page template I ran into a number of different problems when it came to implementing the stylesheet into the actual page.

Firstly, being familiar to html I went for the standard method of inserting this into the page template itself,
<link rel="stylesheet" type="text/css" media="screen, projection" href="...css/pete.css" />

Which on reflection seems ludicrous now, but hey, learning curves and whatnot.

After some head scratching and some research I realised that I had to insert the coding into the actual header, however the page template is using a secondary header, so I tried entering this into the header-secondary.php

<link rel="stylesheet" type="text/css" media="all" href="<?php bloginfo( 'stylesheet_url' ); ?>" />
<link rel="stylesheet" type="text/css" href="<?php bloginfo('pete.css'); ?>" media="screen" />
<?php if(is_page_template('Peter McAllister.php')) :?>
<link rel="stylesheet" type="text/css" href="<?php bloginfo('template_directory'); ?>/pete.css" media="screen" />

But still nothing, if anyone could give me a hand it would be really appreciated!

Regards and thanks in advance, Pete.