What CMS are you using? Is it custom made, or by a company? The reason I ask, is if it's custom made, then it would almost just be easier to use integrate the vb systems into it directly. This will allow you to use the same cookie for everything, which would just be the cookie vb set itself.
I don't mess around with the Remember Me settings, but i just used something like:
Code:
<form action="*forum_url*/login.php" method="post" onsubmit="md5hash(vb_login_password, vb_login_md5password, vb_login_md5password_utf, 0)">
<script type="text/javascript" src="*forum_url*/clientscript/vbulletin_md5.js"></script>
<label for="user">Username:</label><br />
<input name="vb_login_username" size="15" accesskey="u" type="text" /><br />
<label for="pass">Password:</label><br />
<input name="vb_login_password" type="password" size="15" /><br />
<input name="s" value="" type="hidden">
<input name="do" value="login" type="hidden">
<input name="vb_login_md5password" type="hidden">
<input name="vb_login_md5password_utf" type="hidden">
<input type="image" src="http://www.divineshadowsonline.com/images/login.png" accesskey="s" alt="Login">
</form>
All you have to do is find the field value for the Remember Me, and vB's internal settings should do the rest