In regards to creating a more elastic crocheted hat, I offer up the following free patterns from Ravelry (not my designs), stitch patterns, and suggestions:
Free Ravelry patterns with lots of stretch:
Ribbed Crochet Preemie Hat (This is simply the stretchiest hat in crochet existence! It bounces right back, so it never loses it's shape)
Broken Rib Hat (minus the pom pom-style top)
1. hdc in back loop only, crochet flat, seam sides with elastic thread or thru one loop only, turn up bottom, pull yarn through loops around top to close, or join with yarn and sc2tog around until hole closes
2. hdc in blo, next row hdc in flo; back and forth for length, then follow first suggestion
3. hdc in strand below front loop every row (this makes a lovely/reversible, knit-look fabric), then follow suggestions from first
4. use post stitches and chainless foundations
5. If you don't like crocheting hats flat due to the seams, you will really like the elastic thread seaming OR knit the hat in the round using a sc stitch through the back loops only.
1. Use elastic thread for edging/seaming.
2. Keep edging round LOOSE! This seems to be the place in which the hat instantly loses its give/take.
3. Go up a hook size to crochet edging.
4. Use a mock-rib brim band w/elastic thread held with yarn, then pick up stitches around to continue crocheting in the round.
5. Make button tab edging and use bobbles instead of buttons for closing.
These are merely suggestion but ones that I have consistently used whenever I make newborn/baby hats or charity hats for preemies/newborns/babies/toddlers.
1. Super Soft Acryllic
2. Sport Weight
3. Cotton w/some acryllic: Lion Brand's "Cotton Ease" is excellent, but I also really love Hobby Lobby's "I Love This Cotton! Yarn"
4. Sock yarn!
5. Superwash Wools and Extrafine Merino Wool are my 2 faves to use when making hats for people I know don't have a preference.