JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1/themes/ui-lightness/jquery-ui.css">
<div id="dialog-datepicker" title='Select Date of Birth' style="display:none;color: #014061;">
    <div id="dob-datepicker"></div>
    <br />
    <div>Selected Date <strong>(YYYY-MM-DD)</strong>: 
    <div id="strSelectedDate" style="font-weight:bold; font-size: 16px;background-color: #BCE9FA;border: 1px solid #57A3CD;padding: 2px 8px;width:120px;"></div>
    </div>
</div>  


<input type="input" id="Edit-HMODependentBirthDt" />

JavaScript

jQuery(document).on('change', '.ui-datepicker-month', function(){
       alert('test');
});

$().ready(function(){
   
/*
    $('.ui-datepicker-month').live("change", function(e) { 
        $('#strSelectedDate').text("");
    });
    */
        
    
    $('.ui-datepicker-year').live("change", function(e) { 
        $('#strSelectedDate').text("");
    });
    
    
$('#Edit-HMODependentBirthDt').click(function(){

    var currentTime = new Date();
    var curYear = currentTime.getFullYear();
    $selectedDate = "";
    //$selectedDate = $('#Edit-HMODependentBirthDt').val() == "" ? "" : $('#Edit-HMODependentBirthDt').val();
    $( "#dob-datepicker" ).datepicker({ dateFormat: "yy-mm-dd", changeMonth: true, changeYear: true, yearRange: (curYear-65) + ':' + curYear, 
        beforeShowDay: function (date) {
        var today = new Date();
        today.setDate(today.getDate() - 14);
        if (date > today)
            return [false];
        else
            return [true];
       },
        onSelect: function(dateText, inst){
        $selectedDate = dateText;
        $('#strSelectedDate').text($selectedDate);
        }
});

    if($selectedDate != ""){
        $( "#dob-datepicker" ).datepicker("setDate", $selectedDate);
        $('#strSelectedDate').text($selectedDate);
    }else{
        $( "#dob-datepicker" ).datepicker("setDate", "");
        $('#strSelectedDate').text("");
    }

    $( "#dialog-datepicker" ).dialog({
        height: 370,
        width: 240,
        modal: true,
        buttons: {
            "OK": function () {
                $('#Edit-HMODependentBirthDt').val($selectedDate);                                
                $(this).dialog("close");
            },
            "Cancel": function () {
                $(this).dialog("close");
            }
        }
   });
    

});


    
    
});