Hi, I'm sorry to hear the stripes are not working out properly. Designer Pica Pau uses X-shaped single crochet stitches, these are made by yarning under instead of yarning over. I see that an explanation on X-sc wasn't included in the book, but this explanation is from her later books:

"Besides the different look, there are a few more differences
you should know about.
– Size: X-shaped single crochet tends to be much tighter,
so the result will be smaller. Vice versa, the fabric made
using V-shaped single crochet is more fluid/elastic, so the
toy will be softer.
– How the stitches seem to turn around: V-shaped
single crochet stitches move a little in each round, so your
crochet work appears to turn to one side. X-shaped single
crochet is less likely to do this, which will give nicer results
when crocheting jacquard."

To make an X-sc, you insert your hook into the next stitch, yarn under your hook (instead of yarn over), pull the loop through the stitch, yarn over as usual and pull the hook through the loops on your hook.

You can make the stripes using the regular sc stitches as well, but in that case (depending on your personal crochet tension), you might need to make the color changes a bit earlier or a bit later, to make sure the stripes are where you want them to be.

I hope this helps you out, enjoy crocheting!