Zend_Auth::getInstance() will return the instance so you can use it in any controller where you need it , make shure to save the data on successfull login so you shouldn't need a model for authenticate or testing if a user is authenticated . ( having auth in you're model would load unnecesary model clases in memory at times when you whont need them ... , the test if a user is authenticated should be placed at bootstrap )
Edit to reply you're question
make a single controller witch will have actions for authentification and loggout , that way you keep everithing separate , you can call the loggout function with a simple link on you're page and redirect back after logging out to $_SERVER['HTTP_REFERER']; so the user ends up back to the page he was viewing when he clicked loggout .