JSFiddle - React, Tailwind, and code Playground

HTML

<p>Date: <input type="text" id="datepicker"></p>

JavaScript

$(function() {
    var oldGenerateHTML = $.datepicker._generateHTML;
    
    function newGenerateHTML(inst) {
        var html = oldGenerateHTML.call(this, inst);
        var $html = $(html);
        $html.find('[data-handler=prev]').remove();
        $html.find('[data-handler=next]').remove();
        $html.find('[data-handler=selectMonth]').replaceWith('<span class="dummy">Foo</span>');
        return $html;
    }

    $.datepicker._generateHTML = newGenerateHTML;
    
    $( "#datepicker" ).datepicker({
        changeMonth: true,
	    changeYear: true
    });
    
    $("body").on("click",".dummy",function() { 
          var dateString = "01/04/2014";
          $("#datepicker").datepicker("setDate", dateString);
    });
});