Actually I'm not mentioning anything PHP, except pointing the form to the login.php file.
It's all HTML and add lines to vb Post Referrer Whitelist option.
Put this code on your HTML page.
<!-- login form -->
<form action="<POINT TO YOUR VB DIR>login.php?do=login" method="post" onsubmit="md5hash(vb_login_password, vb_login_md5password, vb_login_md5password_utf, 0)">
<script type="text/javascript" src="<POINT TO YOUR VB DIR>clientscript/vbulletin_md5.js?v=364"></script>
<table cellpadding="0" cellspacing="3" border="0">
<tr>
<td class="smallfont"><label for="navbar_username">User Name</label></td>
<td><input type="text" class="bginput" style="font-size: 11px" name="vb_login_username" id="navbar_username" size="10" accesskey="u" tabindex="101" value="User Name" onfocus="if (this.value == 'User Name') this.value = '';" /></td>
<td class="smallfont" colspan="2" nowrap="nowrap"><label for="cb_cookieuser_navbar"><input type="checkbox" name="cookieuser" value="1" tabindex="103" id="cb_cookieuser_navbar" accesskey="c" />Remember Me?</label></td>
</tr>
<tr>
<td class="smallfont"><label for="navbar_password">Password</label></td>
<td><input type="password" class="bginput" style="font-size: 11px" name="vb_login_password" id="navbar_password" size="10" tabindex="102" /></td>
<td><input type="submit" class="button" value="Log in" tabindex="104" title="Enter your username and password in the boxes provided to login, or click the 'register' button to create a profile for yourself." accesskey="s" /></td>
</tr>
</table>
<input type="hidden" name="s" value="" />
<input type="hidden" name="do" value="login" />
<input type="hidden" name="vb_login_md5password" />
<input type="hidden" name="vb_login_md5password_utf" />
</form>
<!-- / login form -->
Then add the domain from your non vb domain to this setting:
vBulletin Options > General Settings > Post Referrer Whitelist > And enter your domain from which your non-vb page reside.