JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.0/jquery.js"></script>
<script src="https://ajax.aspnetcdn.com/ajax/jquery.validate/1.11.1/jquery.validate.js"></script>
<form>
  <label>field one:
    <input name="one" type="text" class="date startdate before-enddate">
  </label>
  <label>field two:
    <input name="two" type="text" class="date enddate after-startdate">
  </label>
</form>

CSS

label {
  display: block;
}

label label.error {
  display: inline-block;
  color: red;
}

input {
  margin: 0 1em 0.5em 0;
}

JavaScript

$.validator.addMethod("beforeEndDate", function(value, element, params) {
  var validator = $(element).closest('form').validate();
  validator.element(params);
  return true;
}, "starting date must be before end date");

$.validator.addMethod("afterStartDate", function() {
  return Date.parse($('.startdate').val()) < Date.parse($('.enddate').val());
}, "end date must be after start date");

$.validator.addClassRules({
  'before-enddate': {
    beforeEndDate: '.enddate'
  },
  'after-startdate': {
    afterStartDate: '.startdate'
  }
});

$('form').validate();