Once your razor view is rendered to the browser, It is just HTML markup. That means, you can use javascript to access the elements in the DOM and update the values as needed.
Keep your script in the main view which holds the 2 partial views.
$(function(){
$("#ButtonInFirstParial").click(function(e){
e.preventDefault();
$("#DivInSecondPartial").html("Updated");
});
});
Also if you declare your javascript variable in a global scope, you can access it in other places also. So if you have a variable like this in your layout page,
<body>
@RenderBody()
<script type="text/javascript">
var global_SiteUrl="Some value i want to access in all pages";
</script>
</body>
You can access it in other views (which uses the above one as the Layout), or js files which are a part of other views who has the layout value set as the above layout.