Thanks for your message!
First off, I would advise against using the Tropy stable and beta release on the same project file. We try to make sure that projects automatically migrate when you open them in newer versions of Tropy, but it's much harder to guarantee that opening an updated/newer Tropy project in an older version of Tropy (which is technically what happens when you open a project file from the beta in the stable release).
Your question aims at a setup where you can work on the same project from both computers, right? This is possible, but there is currently a big limitation: the paths to your photos are stored as absolute paths in your project file. That means, in order to use the same project on different systems, these paths need to be identical. If this is is not possible (e.g., because Windows assigns different drive letters to your USB drive) you can probably work around this using sym links (I'm no Windows user myself, but that's what I'd do on Linux for example).
If it's possible to place your photos in such a way that they are reachable via the same path, we need to use that path in your project. Because consolidating via the UI currently works on a single photo at a time the best way to do this, currently, is to change the paths in your project database. I'd be happy to adjust the paths for you, but you'd have to give me the context of your setup, i.e.: What is the absolute path of your photos on your laptop and on your desktop? And can you set up a sym link folder so that you can have a unique absolute path on both systems?