• We have updated our Community Code of Conduct. Please read through the new rules for the forum that are an integral part of Paradox Interactive’s User Agreement.
In the bottom left you can toggle castles, shields, and units on and off. I might be misunderstanding your exact problem, but this is what I did for a similar problem in the past.
 
The difficulty is that I can't toggle an army on or off. It's always on, and then if I click anywhere near the island I just get the army (if it's mine) or nothing (if it's someone else's). I can't get the province itself.

It is strange that you can't toggle of armies. Can you toggle of shields or castles ?
 
There are 3 icons that you can toggle off in the lower left corner: The fort turns off forts, the shield turns of CoA's, and the sword turns off troops and the fog of war.
 
I think you can see the province coat of arms at the top of the selected army screen and select it from there or move the army away....rugen is a smaller harder island
 
My apologies to all. The sword icon is exactly what I needed to use. I think I saw this when I first started the game, but didn't need it then and by the time I needed it, I had forgotten it. Problem solved.

Well the buttons are very well hidden :)
 
First select your army, then click on the icon to turn off troops in the map - I think your army should still be selected.
 
Ah. I know I landed an army on Bornholm when another army was there once, but I don't remember how. Maybe circle your mouse to discover if a tiny bit of the island is not covered?
 
Ah. I know I landed an army on Bornholm when another army was there once, but I don't remember how. Maybe circle your mouse to discover if a tiny bit of the island is not covered?

This ... even with armies and shields on, all the islands can be clicked ... but Bornholm and Rügen are especially hard to select. You have to find the very tiny part of it that is not covered by the graphics. It can be a bit fiddly, but should be doable. Once you find where the island is accessible, then you know for next time where to click, and it won't be so hard.