I made a square hat for Abbie with a zig-zag puff stitch. I had to make the construction of this hat up as I went, but it's pretty forgiving since it doesn't have any shaping to it. joining the puff stitches in each round was the hard part, but I made it work. this could totally be done as a flat piece and then seamed together, though. I put tassels on the top corners to look like pig tails, and I made some boots with puff stitch flowers on them to match the hat.
Ava got a striped slouchy hat (another pattern I made up as I went) and I added a puff stitch flower to the bottom band. I used Red Heart Soft for all of these hats, which gets even softer when you steam or wash it. I steamed the slouchy part of this hat which made it lay really nice, but I made sure to leave the band at the bottom alone in case it relaxed too much.
Ashton's hat is an earflap beanie that I decided to find an actual pattern for. I used Micah Makes free pattern, but I added an extra row of single crochet to the edge and put a line of fringe on top for a mohawk.