In the attached I remived your bottom chart and replaced it with a container. I made a copy of the bottom chart, and named one Region and the other Segment. I shoved both sheets into that container. And I deleted the titles. (There's a reason for this.)
Then I made a calc that I use as a filter on both sheets. One is set to "Region" and the other to "Segment". Now only one sheet displays at a time depending on which value of the parameter is selected.
This is called sheet swapping.
Next I went to one of the other sheets and edited "Apply to" for the Region and the Segment filters. I applied the respective one to the appropriate sheet.
Now the proper sheet displays, and it has the respective filter activated (and ignores the other.)
I did this in the Using Filter dashboard.
Parameter to Filter Test A.twbx 73.2 KB
Thank you for tackling this and providing a great solution. I have been so close to this that sheet swapping didn't even occur to me. I can see how it will work so I will mark this as a correct answer.