ureech,
тоже самое без плясок с бубнами, если использовать для алтернативного вывода input, а не div.
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>jQuery UI Datepicker - Default functionality</title>
<link rel="stylesheet" href="https://code.jquery.com/ui/1.12.0/themes/base/jquery-ui.css">
<style type="text/css">
#div{
outline: none;
border: none;
width: 350px;
}
</style>
<script src="https://code.jquery.com/jquery-1.12.4.js"></script>
<script src="https://code.jquery.com/ui/1.12.0/jquery-ui.js"></script>
<script>
$(function() {
$("#date_eat").datepicker({
dateFormat: "yy-mm-dd",
altFormat: "'другой формат: 'DD, d MM, yy",
altField: "#div",
onSelect: function(a) {
}
})
});
</script>
</head>
<body>
<p>Date: <input type="text" id="date_eat"></p>
<p>DateAlt: <input type="text" id="div" readonly="readonly"></p>
</body>
</html>