#two:first-child { background: red; }
   #three:last-child { background: lime; }

 <div>

  <script type="text/javascript">
   

    function test() {
      el2 = document.getElementById('two');
      el3 = document.getElementById('three');
      el2.parentNode.insertBefore(el3.nextSibling, el2);
    }

    window.setTimeout("test()", 100);
   
  </script>

  <div><p id="two">This line should be unstyled. (2)</p><p id="three">This line should have a green background. (3)</p><p>This line should be unstyled. (4 moving to 1)</p></div>

 </div>