WP Query Compare cutting off last 2 dates

It looks like your meta_query is nested within an extra array. Aside from that, the code looks valid.

Hope this helps:

$argsTwo = array(
  'post_type' => 'event',
  'meta_key' => '_event_information_year_select',
  'orderby' => 'meta_value',
  'order' => 'ASC',
  'meta_query' => array(
    'relation' => 'AND',
    array(
      'key'     => '_event_information_year_select',
      'value'   => 1999,
      'compare' => '>'
    ),
    array(
      'key'     => '_event_information_year_select',
      'value'   => 2003,
      'compare' => '<='
    )
  )
);