What is this piece of children's playground apparatus called?
Solution 1:
Did you get the picture from here?
It's called an "Inclusive Spinning Dish" or a "Dish Roundabout"
Solution 2:
I would probably call it a "cup" or "spinning cup", and I most people would understand, if they had seen it.
Solution 3:
I can't see any reason to call it anything different from the manufacturers (linked elsewhere here) who describe it as a Spinning Dish. The additional attribute of 'inclusive' seems to be more of an advertising adjective.