Views : custom table with relationship is not queried
Instead of adding the fields manually, you should populate the instance variable additional_fields. From the views documentation:


  additional fields: An array of fields that should be added to the query for some purpose. The array is in the form of: array('identifier' =&gt; array('table' =&gt; tablename, 'field' =&gt; fieldname);


Looking through some of the implementations out there indicates that your code should look something like this:

class MYCLASS extends views_handler_field {
  function construct() {
    parent::construct();

    $this-&gt;additional_fields['ALIAS1'] = array(
      'field' =&gt; 'COLUMN1',
      'table' =&gt; 'MYTABLE',
    );
    $this-&gt;additional_fields['ALIAS2'] = array(
      'field' =&gt; 'COLUMN2',
      'table' =&gt; 'MYTABLE',
    );
  }

  function query() {
    $this-&gt;ensure_my_table();
    $this-&gt;add_additional_fields();
  }

  function render($values) {
    $alias1 = $this-&gt;get_value($values, 'ALIAS1');
    $alias2 = $this-&gt;get_value($values, 'ALIAS2');
    ...
  }
}