If I understand correctly, you use js to make an ajax request to a django view. That view is supposed to return an html snippet which should be rendered within a div of the calling window. However, if the auth token has expired, the view will return a 302 redirect and you want the browser to follow this redirect.
If that's your problem indeed, you can read these questions
How to manage a redirect request after a jQuery Ajax call
How to get response status code from jQuery.ajax?
which answer exactly your question (especially the first question). JQuery won't handle a redirect response the way you expect it to, it just follows the redirect and returns the new html.
You could try one of the above solutions, but let me add my 2 cents. Since you're in control of what the server will return, instead of an HttpResponseRedirect
try to render a django template containing a script like this:
<script>
window.location.href = "/my-login-url"
</script>
That way jQuery (which expects an html response) will evaluate the script and redirect users to the login url.