How do keep 2 iMacs from detecting each other as displays

We have 2 iMacs and an iPad arranged on a desk in close proximity: iMac--iPad--iMac.

Recently something has started happening where one of the iMacs automatically detects the iPad as well as the 2nd iMac as additional screens to use for its own purposes and when I use the mouse on the rightmost iMac it seemlessly travels to the iPad on the left and then the other iMac on the very laft.

This is not what we want. We want each device to be its own devicew with its own keyboard and mouse that only controls the device itself.

We can use the System Preferences/Displays panel to get it back to only use its own screen, but, without fail, either on the next startup or at some random time during the day, it will again decide that it wants to consider the other 2 devices as its own display and will revert to a multi-screen setup.

While I think it's an extremely cool feature that this is even possible, it is not what we want in this case: How do I tell my Mac to stop detecting the displays of the other devices and leave them alone, permanently (or until I manually change the display settings)

Any ideas?