I carefully laid out the pieces of the crown so the "stretch" would be going across. One piece of the red fat quarter seemed a little stretchier than the other. The black had less stretch because of the embroidery. I also cut the interfacing in two pieces, with a small overlap. I wanted to see if this worked on my own hat before doing it on one for someone else! I totally think it worked.
I sewed the red brim on first. I had pinned the 1/4 marks, and it went fine until the last 1/4 section. I ended up with more than an inch extra brim. Instead of panicking and ripping it out immediately, I set it aside and sewed the black brim on. It went on almost entirely perfect, maybe 1/2" brim left over. So I ripped off the red brimmed and tried again, had to try a few times and I think in the end I did have to take in the brim seam a little bit--1/4" from each side of the brim seam? (I left the outer edge the same, but tapered the seam towards the crown). The brim looks a little pulled in a few places. I didn't have a red thread that matched close enough, so I used white.
During the process, a few people mentioned it looks like Minnie Mouse. Then, when it was finished...I realized that I also have a red nightgown with white polka dots. Yup. My sun hat matches my nightgown.