Make To and From date range picker using jQuery UI
Instead of destroying and recreating the datepickers, use the (3rd) option method (e.g. .option('maxDate', selectedDate)) to set the minDate/maxDate options when appropriate. 

Also, by utilizing the onSelect option, which receives as arguments the selected date and the datepicker instance, instead of using an onChange handler, MomentJS can be eliminated. 

Lastly, the two id selectors can be combined in the same jQuery call:

$('#Start, #End').datepicker(datepickerConfiguration);


See the simplified code below.

Another option might be to consider a daterange picker UI widget like this one but perhaps the current UI is desired.



//use this one handler for both Start and End Date pickers
var onDateSelect = function(selectedDate, input) {
  if (input.id === 'Start') { //Start date selected - update End Date picker
    $("#End").datepicker('option', 'minDate', selectedDate);
  } else { //End date selected - update Start Date picker
    $("#Start").datepicker('option', 'maxDate', selectedDate);
  }
};
var onDocumentReady = function() {
  var datepickerConfiguration = {
    dateFormat: "dd/mm/yy",
    onSelect: onDateSelect
  };
  ///--- Component Binding ---///
  $('#Start, #End').datepicker(datepickerConfiguration);
};
$(onDocumentReady);  // jQuery DOM ready callback registration
&lt;link rel="stylesheet" href="//code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css"&gt;
&lt;link rel="stylesheet" href="/resources/demos/style.css"&gt;
&lt;script src="https://code.jquery.com/jquery-1.12.4.js"&gt;&lt;/script&gt;
&lt;script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"&gt;&lt;/script&gt;
&lt;p&gt;Start Date: &lt;input type="text" id="Start"&gt;&lt;/p&gt;
&lt;p&gt;End Date: &lt;input type="text" id="End"&gt;&lt;/p&gt;