How do I force a reload after a CiviCRM summary action?
I know this is like two years later but I just went through a really similar problem and there's no answer here yet...

First off Coleman posts a good answer here for lots of situations: Can I update/requery a custom field that got changed via another field on the same page?

I couldn't get this to work with certain ajax-y elements like the "disable" button under the relationships tab (we had a tab of custom fields that calculate values from other contacts based on relationships, when those relationships aren't active the data recalculates and we want it to display current values).

I worked around this by adding a JS file in hook_civicrm_summary, where the JS asks our custom data to reload every time you click the tab, so you always get current values at a slight performance cost. I'd imagine you could do this with an inline header as well:

  CRM.$(function($) {
    $('#ui-id-22').click(function(){
      CRM.refreshParent($('#Site_Demographics_1_2760'));
    });
  });


Where '#ui-id-22' was our tab link and '#Site_Demographics_1_2760' was the panel we wanted to update.