Activate 1 macro group for 1 action but also deactivate all the others for 1 action?

That is correct, the Show/Hide palette accepts ONLY a Hot Key.
You can make a request that it be changed, but for now you will need to use the tool you have.

I assume you have a normal keyboard, so surely it would not be too hard come up with two keystrokes that you could use for this.

But here is a direct solution for you. Create Macro outside of either of those Macro Groups, and use a USB Device Key to Show/Hide the palette of the desired MG:

image

Pressing the key gives this:
image

Will that work for you?