Editing a gallery using JuiceboxBuilder-Pro relies on there being a local copy of the gallery available.
JuiceboxBuilder-Pro cannot edit a gallery online.

If you want to edit a single gallery using two different computers, then, each time you edit the gallery on one computer, I'd recommend storing the entire gallery somewhere so that it can be accessed by the other computer. Perhaps copy the gallery folder to a USB flash drive or zip the complete gallery folder and upload it somewhere so that you can easily download it and work on it from your second computer.

I don't know how important it is for you to manage a gallery from different locations but you might be interested in another one of our products: Showkase.

Showkase is a PHP web application (installed on your web server) which allows you to create a complete portfolio web site (integrating multiple galleries) online. However, you can use Showkase in its Gallery Manager theme to create and edit galleries (which you can embed into any web pages throughout your website) online through a web browser interface. You'd be able to log into your Showkase site from any computer and edit your gallery directly online (without the need to upload any modified gallery files via FTP). You can also import existing galleries (created with JuiceboxBuilder-Pro) into your Showkase site so that you can then manage them from within the application's interface.

Please feel free to take a look around the Showkase interface by logging into the Live Demo Admin.

Showkase can be purchased as Showkase-Standard (which comes with Juicebox-Lite and SimpleViewer-Standard, the free versions) or Showkase-Pro (which comes with Juicebox-Pro and SimpleViewer-Pro). The only difference between Showkase-Standard and Showkase-Pro is the bundled viewers.
As you already have Juicebox-Pro, you could purchase Showkase-Standard and integrate your Juicebox-Pro files following the Installing a Pro Viewer instructions.