<p><input name="submit" type="submit" id="submit" tabindex="5" value="Valider le commentaire" />
<?php comment_id_fields(); ?>
</p>
<?php do_action('comment_form', $post->ID); ?>

Si c'est un CMS regardes plutôt du côté du template de la page.
Je ne sais pas comment fonctionne les plugins pour Wordpress mais tu auras surement une partie qui apparait dedans.
Ainsi que le bouton submit, il te suffira de le déplacer.

<span class="art-button-wrapper"><span class="art-button-l"> </span><span class="art-button-r"> </span>
		<input class="art-button" type="submit" name="submit" tabindex="5" value="<?php _e('Submit Comment', THEME_NS); ?>" />
	</span>

<p><textarea name="comment" id="comment" cols="40" rows="10" tabindex="4"></textarea></p>
<p>
	<span class="art-button-wrapper"><span class="art-button-l"> </span><span class="art-button-r"> </span>
		<input class="art-button" type="submit" name="submit" tabindex="5" value="<?php _e('Submit Comment', THEME_NS); ?>" />
	</span>
    <?php comment_id_fields(); ?>
</p>
<?php do_action('comment_form', $post->ID); ?>
</form>
<?php endif;?>
<?php 
  art_post_box('', ob_get_clean(), 'respond');

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.art-button-wrapper a.art-button:link,
.art-button-wrapper input.art-button,
.art-button-wrapper button.art-button
{
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  color: #F9FAFB !important;
  width: auto;
  outline: none;
  border: none;
  background: none;
  line-height: 36px;
  height: 36px;
  margin: 0 !important;
  padding: 0 26px !important;
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  cursor: default;
}

.art-button img, .art-button-wrapper img
{
  margin: 0;
  vertical-align: middle;
}

.art-button-wrapper
{
  vertical-align: middle;
  display: inline-block;
  position: relative;
  height: 36px;
  overflow: hidden;
  white-space: nowrap;
  width: auto;
  margin: 0;
  padding: 0;
  z-index: 0;
}

.firefox2 .art-button-wrapper
{
  display: block;
  float: left;
}

input, select, textarea
{
  vertical-align: middle;
  font-family: Arial, Helvetica, Sans-Serif;
  font-size: 13px;
}

.art-block select 
{
    width:96%;
}

.art-button-wrapper.hover .art-button, .art-button-wrapper.hover a.art-button:link, .art-button:hover
{
  color: #7F5305 !important;
  text-decoration: none !important;
}

.art-button-wrapper.active .art-button, .art-button-wrapper.active a.art-button:link
{
  color: #FFFFFF !important;
}

.art-button-wrapper .art-button-l, .art-button-wrapper .art-button-r
{
  display: block;
  position: absolute;
  height: 118px;
  margin: 0;
  padding: 0;
  background-image: url('images/button.png');
}

.art-button-wrapper .art-button-l
{
  left: 0;
  right: 18px;
}

.art-button-wrapper .art-button-r
{
  width: 425px;
  right: 0;
  clip: rect(auto, auto, auto, 407px);
}

.art-button-wrapper.hover .art-button-l, .art-button-wrapper.hover .art-button-r
{
  top: -41px;
}

.art-button-wrapper.active .art-button-l, .art-button-wrapper.active .art-button-r
{
  top: -82px;
}

.art-button-wrapper input
{
  float: none !important;
}
/* end Button */

Le bouton a quelque chose à voir avec le code de vote ou aucunement ?
S'ils sont en relation c'est que c'est un problème de CSS.

S'ils n'ont rien à voir, c'est encore un problème de CSS mais qu'on peut régler autrement.
A savoir en mettant le bouton submit en dessous.
Tu dois avoir un include() qui n'est pas au bon endroit.