When that button is clicked on the previous page, I'd store the value I needed in a page or application item. Then that would be the source you use on the new page's displayed.
If it's not possible to store it in the button code, then create a Dynamic Action based on the button click and execute the code there to store the value. I suppose you could even store in an item, like :P2_VALUE_I_WANTED_DISPLAYED, so it's stored in a Page 2 item.
Depending on what your button does, you could let it submit the page and then provide an after submit branch and set a value in the target page. Or have this in a redirect, when you choose "Redirect to page in this application" as button action you can also set items. I'm not sure why you'd make the hop through the application item here?