Question

How can I trigger second hover function?

$('#adm1n-toolbar').hover(
    function() {
        ...
    },
    function() {
        ...
    }
);

$('#adm1n-toolbar-content select').change(function(e) {
    ...
    $('#adm1n-toolbar').trigger('mouseout');
});

mouseout or mouseleave does not work.

Answer 1

It works just fine if you use mouseleave which is what hover uses behind the scenes

demo:

$('#adm1n-toolbar').hover(
  function() {
    console.log('in');
  },
  function(e) {
    $(this).fadeOut('fast').fadeIn('fast');
  }
);

$('#adm1n-toolbar-content select').change(function(e) {
  $('#adm1n-toolbar').trigger('mouseleave');
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div id="adm1n-toolbar">toolbar</div>

<div id="adm1n-toolbar-content">
  <select multiple>
    <option>option 1</option>
    <option>option 2</option>
    <option>option 3</option>
    <option>option 4</option>
  </select>
</div>