A nested div with a z-index will never be higher than an element outside of the parent. This article explains it well. what you could do is move the nested div outside and toggle the visibility when .ui-layout-toggler-north
is clicked. See this JSFiddle
$('.ui-layout-toggler-north').click(function(){
$('#chosen_select').toggleClass('hide');
});
Note: I put a select element in the .ui-layout-north div as a placholder for the actual "chosen select" element.