Send webbrowser data to another webbrowser. (python prefereable)

i have an unlimited internet connection in my house and a limited internet conecction in the school.

I want to make a webbrowser (or something like that) that navigate from my house, get the data (incluiding the streamings) and resent it to my browser in the school.

In python, using webkit, a webbrowser can be created easily and navigate youtube and other pages, i want to recreate that navigation in other webbrowser (the one connected in my school).

School browser ----> send request to program or another webbrowser ---> get page data (incluiding streaming) -----> tunnelling ---> sent to school browser.

Its something like to do a remote webbrowser.

thanks in advantages.