Admin page to show 2 blocks (or page+block) with 1 filter that affects both blocks
The described scenario doesn't need custom coding as it is shipped with Drupal 7 Views module.

The approach to use a views block in a views page that shares the same filter can be done using the "Attachment" view.

You can find more about views attachment here

Also, there is an answer to place the attachment in a different page region here

Hope this answers your question.