How can I change the redirect that happens after a node is edited?
You have a few options.

If you want to install a module and use a GUI you should be able to do that with Rules.  Just install the module, and setup a new rule to react on saving new content. 

If you do not plan on using Rules for anything else, it is probably wiser to just use a hook_form_alter in your custom module.  Just edit the forms $form_state['redirect'] in a submit callback. Something like:

function test_form_alter(&amp;$form, &amp;$form_state, $form_id){
  if($form_id=='MY_FORM') {
    array_push($form['#submit'], 'test_userlogin_submit');
  }
}

function test_userlogin_submit(&amp;$form, &amp;$form_state){
  $form_state['redirect'] = 'MY/NEW/PATH';
}