How to build a url to an (AJAX driven) exposed filter?
If I understood well, once I face the same situation than you, the module Views Filter Harmonizer help me to solve my issue.

From the module's page:


  Views Filter Harmonizer solves an operational foible with the Views
  module regarding filtering.
  
  Normally, when a Views field has been assigned both an exposed filter
  and a contextual filter, then both filters get applied to the View's
  results set -- always. This is not configurable behaviour. It's
  hard-coded.