codeigniter redirect to different controller
First of all, you are doing a very poor job of checking if the user is authenticated (just passing username/pass to model isn't best, should process / check it before sending to model).
You can make redirects easily by including the helper 'URL' and simply use:
redirect('/controller/method');
or in a real world example:
redirect('/main');
There is another way but similar to redirect(), if your controller is Rest controller
You can use rest client in another controller to call methods on the server controller
redirect('controller/function');
For example you can have redirect('auth/login');
with routes as
$route['auth/login'] = 'auth/auth/index';