Load .php file into div using ajax

Loading a PHP file the way you try to do it is still a direct access to the file. What you should do is “run” the file during the processing of the ajax request on the server side, and send the result back to the browser. Than you insert the result into the div.

Your code should be something like

add_action('wp_ajax_tps_refresh_cart_display', 'tps_refresh_cart_display');
add_action('wp_ajax_nopriv_tps_refresh_cart_display', 'tps_refresh_cart_display');
function tps_refresh_cart_display() {

    // Grab php file output from server
    ob_start();
    include('path-to-file.php');
    $result['content'] = ob_get_contents(); 
    $result = json_encode($result); // use wp_send_json instead to make this shorter
    echo $result;
    die();
}

and then on the JS you should do something like

success: function(response) {
                //load the fetched "result" of the php file into the div
                $('#content').insert(response.content);
            }