I suggest getting a barmod that keeps track of keybindings on its own. I use Trinity UI. Then you could copy it and the saved variable over to the other computer and place the bars to fit the other screen. Then you will have both of the same keybinds...
OPTION TWO
You could use trinity UI to have a layout on your Desktop then make a layour on your laptop. Once you place all the skills on your desktop you can 'choose to view the
Action buttons ID' Once you do this you can set the Id's on the laptop.
This will allow you to place or create any amount of different arrangments. But when you change once button on one the SAME button will change on the other one. So if you match up the keybinds then no matter what arrangement you have you will keep both computers in sync.