Redirect users based on their roles, is_admin()

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.