> Specifically, I'd like to create a plugin to echo the following in the
> header immediately after the default stylesheet

The preferred way is to *enqueue* it, with the default/main stylesheet as the *dependency*.

Here's a demo plugin, with the structure:

    + plugins/
    |
    +--+ my-ie-style/
       |    
       +--+ my-ie-style.php
       |
       +--+ css/
          |
          +--+ ie.css

where the `my-ie-style.php` file is:

    <?php
    /**
     * Plugin Name: Demo - My IE style
     * Plugin URI:  http://wordpress.stackexchange.com/a/85496/26350
     * Description: Enqueue With IE conditional, depending on the main-style stylesheet
     * Author:      wpse
     * Version:     1.0.0
     */
    add_action( 'wp_enqueue_scripts', function()
	{
		// Register
        wp_register_style( 
           'my-ie-style',                                 // handle
           plugin_dir_url( __FILE__  ) . 'css/ie.css',    // file
           [ 'main-style' ],                              // dependency    <-- ADJUST THIS!
           '1.0.0',                                       // version
           'all'                                          // media
        );

		// Enqueue
		wp_enqueue_style( 'my-ie-style' );
		
		// Add IE conditional
		wp_style_add_data( 
            'my-ie-style',  // handle
            'conditional',  // key ('conditional', 'rtl', 'suffix', 'after', 'alt', 'title')
            'IE'            // value
        );
    } );

This will generate the following within the `<head>` tag:

    <link rel='stylesheet' 
          id='main-style-css'  
          href='http://example.tld/wp-content/themes/mytheme/style.css?ver=4.5.3' 
          type='text/css' 
          media='all' />

    <!--[if IE]>
    <link rel='stylesheet' 
          id='my-ie-style-css' 
          href='http://example.tld/wp-content/plugins/my-ie-style/css/ie.css?ver=1.0.0' 
          type='text/css' 
          media='all' />
    <![endif]-->

where our *custom* IE stylesheet loads after the *main* stylesheet.

Hopefully you can adjust it to your needs.