If I understand correctly you want to rip the content from a DIV on one site and display it on another. There are several issues with this, but I'll focus on the technological aspect and assume you are acting in good faith with pulling the content.
The real issue you're running up against here is that you don't have access to DOM elements of pages that haven't loaded yet. As such you need to tell the browser to load the data for that page so that you can access the elements that should have loaded on the page and then pull the information out. JQuery has a nice little method to help with that called .load() (http://api.jquery.com/load/).
As an important side note however you can't do this as all modern broswers forbid cross site access in such a manner:
From the JQuery .load() page:
Additional Notes:
Due to browser security restrictions, most "Ajax" requests are subject to the same origin policy; the request can not successfully retrieve data from a different domain, subdomain, or protocol.
And check out:
http://en.wikipedia.org/wiki/Same_origin_policy
One more bit of warning. If you don't control the code on the other site you are potentially exposing yourself to serious security issues so only do this in situations where you have control of the other site or for some reason have absolute faith in that site. Alternatively you should try to, if available, use APIs for the sites/services you are trying to get data from.