You could proceed like that :
add_filter("login_redirect", "wpse_113875_login_redirect", 10, 3);
function wpse_113875_login_redirect($redirect_to, $request, $user) {
if(is_array($user->roles))
if(in_array('administrator', $user->roles))
return site_url('/wp-admin/');
return home_url();
}
This will use the WP login system and redirect users according to their role after login. I think this is easier than building your own script in this case. You could easily add some button or link in front-end to the WP login page. Hope this helps.