You can use your core on the the other Mac, just sign it will ask for you to deauthorise the other one just do it and your up and running. If you have a backup of your database restore it to that code an job done.
I don’t remember how exactly the UI looks, but when signing into your temporary Core you should be given the option to either unauthorize your regular Core (there should be a button for that) OR to buy an additional subscription. You only need a second subscription if you want to run two cores at the same time. Otherwise you may switch the subscription between two cores. See here: