Tenta o seguinte: no seu arquivo da index, coloque:
<?php
define(’WP_USE_THEMES’, false);
require(’../blog/wp-blog-header.php’);
?>
Isso teoricamente vai te deixar acessar as funcionalidades do WP (nunca testei).
Depois, onde vc quer que apareça o login, coloque o código abaixo (tirado daqui: http://www.wpdesigner.com/2007/07/09/how-to-place-a-login-form-in-the-sidebar/)
Você pode também apenas estudar o código e adaptar para o seu formulário já existente.
Espero que funcione! (mas eu concordo com o vteixeira!)
<li>
<?php global $user_ID, $user_identity, $user_level ?>
<?php if ( $user_ID ) : ?>
<h2>Control panel</h2>
<ul>
<li>Identified as <strong><?php echo $user_identity ?></strong>.
<ul>
<li><a href="<?php bloginfo('url') ?>/wp-admin/">Dashboard</a></li>
<?php if ( $user_level >= 1 ) : ?>
<li><a href="<?php bloginfo('url') ?>/wp-admin/post-new.php">Write an article</a></li>
<?php endif // $user_level >= 1 ?>
<li><a href="<?php bloginfo('url') ?>/wp-admin/profile.php">Profile and personal options</a></li>
<li><a href="<?php bloginfo('url') ?>/wp-login.php?action=logout&redirect_to=<?php echo urlencode($_SERVER['REQUEST_URI']) ?>">Exit</a></li>
</ul>
</li>
</ul>
<?php elseif ( get_option('users_can_register') ) : ?>
<h2>Identification</h2>
<ul>
<li>
<form action="<?php bloginfo('url') ?>/wp-login.php" method="post">
<p>
<label for="log"><input type="text" name="log" id="log" value="<?php echo wp_specialchars(stripslashes($user_login), 1) ?>" size="22" /> User</label><br />
<label for="pwd"><input type="password" name="pwd" id="pwd" size="22" /> Password</label><br />
<input type="submit" name="submit" value="Send" class="button" />
<label for="rememberme"><input name="rememberme" id="rememberme" type="checkbox" checked="checked" value="forever" /> Remember me</label><br />
</p>
<input type="hidden" name="redirect_to" value="<?php echo $_SERVER['REQUEST_URI']; ?>"/>
</form>
</li>
<li><a href="<?php bloginfo('url') ?>/wp-register.php">Register</a></li>
<li><a href="<?php bloginfo('url') ?>/wp-login.php?action=lostpassword">Recover password</a></li>
</ul>
<?php endif // get_option('users_can_register') ?>
</li>