Problem sorting events by Term Reference
It would seem like your link is simply rendering the taxonomy term usage page (that comes standard with Drupal). What I would recommend is creating Views with Contextual Filters (the filter could be the name of the taxonomy term, in this case nursing-home). 

Once you have your Views with Contextual Filters built (with a set link, such as /events/) then you can simply rewrite the result of the term field (i.e. display it as plain text and then rewrite) using tokens for the machine name of the term and provide it as a link.

Does this make sense?