jQuery Mobile 2-page Base Fiddle

HTML

<script src="http://code.jquery.com/mobile/latest/jquery.mobile.min.js"></script>
<link rel="stylesheet" href="http://code.jquery.com/mobile/latest/jquery.mobile.min.css">
<script src="https://code.jquery.com/jquery-2.2.1.min.js"></script>
<div id="groups">
  <fieldset id="TV_fieldset" data-mini="true" data-role="controlgroup" data-type="horizontal">

    <legend>Limit:</legend>

    <input type="radio" name="Limit_Total" id="Limit_Total_1" value="1">
    <label for="Limit_Total_1">One</label>

    <input type="radio" name="Limit_Total" id="Limit_Total_2" value="2">
    <label for="Limit_Total_2">Two</label>

    <input type="radio" name="Limit_Total" id="Limit_Total_3" value="3">
    <label for="Limit_Total_3">Three</label>

    <input type="radio" name="Limit_Total" id="Limit_Total_4" value="4">
    <label for="Limit_Total_4">Four</label>

    <input type="radio" name="Limit_Total" id="Limit_Total_5" value="5">
    <label for="Limit_Total_5">Five</label>

    <input type="radio" name="Limit_Total" id="Limit_Total_6" value="6">
    <label for="Limit_Total_6">Six</label>
  </fieldset>

  <fieldset id="Child_fieldset" data-mini="true" data-role="controlgroup" data-type="horizontal">

    <legend>Child:</legend>

    <input type="radio" name="Child_Total" id="Child_Total_0" value="0" checked>
    <label for="Child_Total_0">None</label>

    <input type="radio" name="Child_Total" id="Child_Total_1" value="1">
    <label for="Child_Total_1">One</label>
  </fieldset>

  <fieldset id="Second_Child_fieldset" data-mini="true" data-role="controlgroup" data-type="horizontal">

    <legend>Second Child:</legend>

    <input type="radio" name="Second_Child_Total" id="Second_Child_Total_0" value="0" checked>
    <label for="Second_Child_Total_0">None</label>

    <input type="radio" name="Second_Child_Total" id="Second_Child_Total_1" value="1">
    <label for="Second_Child_Total_1">One</label>
  </fieldset>

  <fieldset id="Third_Child_fieldset" data-mini="true"...

JavaScript

$('div#groups').on('change', 'input[name="Limit_Total"]', updateUI);
$('div#groups').on('change', 'input[name="Child_Total"]', updateUI);
$('div#groups').on('change', 'input[name="Second_Child_Total"]', updateUI);
$('div#groups').on('change', 'input[name="Third_Child_Total"]', updateUI);
$('div#groups').on('change', 'input[name="Fourth_Child_Total"]', updateUI);
$('div#groups').on('change', 'input[name="Fifth_Child_Total"]', updateUI);


function updateUI(element) {
  var limit = parseInt($('input[name="Limit_Total"]:checked').val(), 10);

  // Children
  var childCount = parseInt($('input[name="Child_Total"]:checked').val(), 10);
  var secondChildCount = parseInt($('input[name="Second_Child_Total"]:checked').val(), 10);
  var thirdChildCount = parseInt($('input[name="Third_Child_Total"]:checked').val(), 10);
  var fourthChildCount = parseInt($('input[name="Fourth_Child_Total"]:checked').val(), 10);
  var fifthChildCount = parseInt($('input[name="Fifth_Child_Total"]:checked').val(), 10);

  // Totals
  var totalChildern = childCount + secondChildCount + thirdChildCount + fourthChildCount + fifthChildCount;


  // // Enable the correct combination of children
  $('input[name*="Child_Total"]').not(element).checkboxradio('disable').checkboxradio('refresh');
  for (var i = 0; i <= 6; i++) {
    if (i <= (limit - totalChildren)) {
      $('input[id$="Child_Total_' + i + '"]').not(element).checkboxradio('enable').checkboxradio('refresh');
    } else {
      $('input[id$="Child_Total_' + i + '"]').not(element).attr('checked', false).checkboxradio('refresh');
    }
  }
}