Ok, I figured it out. I just moved the Remember Me Label to show up right after the password field before the login button. For anyone else wanting a layout similar to mine. Here is the rearranged code.
<form id="navbar_loginform" action="login.php?{vb:raw session.sessionurl}do=login" method="post" onsubmit="md5hash(vb_login_password, vb_login_md5password, vb_login_md5password_utf, {vb:raw show.nopasswordempty})">
<fieldset id="logindetails" class="logindetails">
<div>
<div>
<input type="text" class="textbox" name="vb_login_username" id="navbar_username" size="10" accesskey="u" tabindex="101" value="<vb:if condition="$username">{vb:raw username}<vb:else />{vb:rawphrase username}</vb:if>" />
<input type="text" class="textbox default-value" tabindex="102" name="vb_login_password_hint" id="navbar_password_hint" size="10" value="{vb:rawphrase password}" style="display:none;" />
<input type="password" class="textbox" tabindex="102" name="vb_login_password" id="navbar_password" size="10" />
<label for="cb_cookieuser_navbar"><input type="checkbox" name="cookieuser" value="1" id="cb_cookieuser_navbar" class="cb_cookieuser_navbar" accesskey="c" tabindex="103" /> {vb:rawphrase remember_me}</label>
<input type="submit" class="loginbutton" tabindex="104" value="{vb:rawphrase log_in}" title="{vb:rawphrase enter_username_to_login_or_register}" accesskey="s" />
That code should give you something that looks like the following.
Attachment 117074