Short answer is: you can't do all of what you're asking (at least not without getting into custom geocoding)
You also can't have a click action change the level of detail on the same sheet that you are clicking.
The reason tableau doesn't recognize your regions is because they're custom values. There is a hierarchy implied here so you can leverage that at least. if you put country on detail and then region on color you'll get a map that shows your regions by color. Then create a calc of:
if last() = 0 then window_sum(sum(value)) end
place this calc on your text shelf of your marks. Set the compute using to "Country" on that field.
This should give you a map that looks like the following (South Pacific seems weird in the data)
You can then create another map that has color at the level of country instead of region and value on text.
This can be a target for a click action. So for example you would click on N. American above and the target chart would show the following:
Your click action would look like this:
forum6.twbx.zip 119.9 KB
Thank you Aaron. This helps me a lot.