Baste them in place. Just trust me on this okay? It's the only way to make them behave and stay where they are supposed to.
After pinning really well, sew two squares together. Then the other two, pressing seams OPEN. The center of the pinwheel becomes too bulky if you don't press them OPEN. Really.
Now stitch both halves of the block together and this is what you have!
You can really get some good lift in the pinwheel blades if you get your iron in there and take out the creases that formed when you were assembling the block.
This is what the back side looked like after quilting. Looks so summery, doesn't it?
Blessing to you!