A prove that that is Peach' castle, is that in the final stage in that tournament Peach' castle can be seen. That would make sense.
Now this, in the second tournament(Flower cup) the final stage is called Daisy's garden.
So that could possibly mean that this mill and ground is property of Daisy.
Prove is that the ground of this tournament is filled with flowers, and(again) the final stage is Daisy's garden. Tennis-wear Daisy is unlocked on this tournament. And, the tournament is called: FLOWER cup.
This could be true!