I did it differently, and the kingdom window opens normally, but when skipping a turn, the button doesn't open the window.
At first, I thought about launching it in a newly created window, but it didn't work inside. And this is just a copied button. It's absolutely the same as the one on the main screen. I don't know how to make the duplicate button open the window while skipping a turn. Maybe it's not possible because it's another player's turn.
Most likely, the "priority" of the screens is higher for the skip turn screen, so the copied button also cannot be clicked, just like the one on the main screen.