You need to use script to expand all parent collapsibles of the target anchor, and then scroll the page to that anchor:
<a href="#nestedAnchor1" class="btnGO1">Go to anchor in Nested Child in Section 1</a><br>
<a href="#nestedAnchor2" class="btnGO1">Go to anchor in Nested Child in Section 2</a>
$('.btnGO1').on('click', function() {
var elem = $(this).prop("href");
elem = elem.substr(elem.lastIndexOf("#"));
var $anch = $(elem);
//expand all parent collapsibles
$anch.parents('[data-role="collapsible"]').collapsible('expand');
//scroll to anchor
var top = $anch.offset().top;
$.mobile.silentScroll( top );
return false;
});
Updated FIDDLE