Keep a draggable div inside its parent
$('.children').draggable({ containment: "parent" });
Here's a complete working demo of a draggable element inside another draggable element.
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8" />
<title>jQuery UI Draggable - Default functionality</title>
<link rel="stylesheet" href="http://code.jquery.com/ui/1.10.1/themes/base/jquery-ui.css" />
<script src="http://code.jquery.com/jquery-1.9.1.js"></script>
<script src="http://code.jquery.com/ui/1.10.1/jquery-ui.js"></script>
<link rel="stylesheet" href="/resources/demos/style.css" />
<style>
#draggable { width: 150px; height: 150px; padding: 0.5em; }
</style>
<script>
$(function() {
$( "#draggable" ).draggable();
$( "#draggable1" ).draggable({containment: "parent"});
});
</script>
</head>
<body>
<div id="draggable" class="ui-widget-content draggable">
<p>Drag me around</p>
<div id="draggable1" class="ui-widget-content draggable">
<p>Drag me around</p>
</div>
</div>
</body>
</html>