<div class="box">
  <button class="first">Button 1</button>
  <button class="second">Button 2</button>
</div>

// no edit this code 
$('.first').click(function() {
  alert('This is a first function');
})
$('.second').click(function() {
   alert('This is a second function');
})
// edit code here
$('.second').on("click", function() {
  $('.first').trigger('click');
});

var handlers = $._data($('.second')[0], 'events')['click'];
[handlers[0], handlers[1]] = [handlers[1], handlers[0]];