Hi Frushvad, welcome to the community!
I wondered if this guide might help you get started with that type of setup? There is also this guide which explains how to send a trigger action from one player to another, which might also be worth looking at, if you want one player to trigger another.
If you add the same action web hook trigger to each layout showing on each display, which will force them to navigate to the layout that contains the animation/media that you want to show, then you could set up your button using one of the methods described in the guide to send that trigger code to the displays.
The person presses the button, that sends a web hook trigger code to each display, which in turn switch to showing the animation layout, then all return to the previous schedule when it is complete.
I hope this helps you set this up. Also I really like the idea, sounds like a good use of interactive actions.
Many Thanks.