How can Wordpress user edit Organisation details?
there is another option you might not know about. Users can be given access to their "My Contact Dashboard" eg at civicrm/user?reset=1 (in Drupal it is at that path).

And if X has permissioned relationship over Y, and if you have not unset it from /civicrm/admin/setting/preferences/display?reset=1 then X should see Y listed, and should be able to 'edit' (some of) their details. hth