What are you supposed to do with the crochet border? Is it only the white on the very edge? Also how is the neck finished? Does the neck have some garter or ribbing and then the crochet or what? If the fronts don't have any crochet but that one little bit of white along the edge it will probably not be enough to tame all of the curl. Since you have everything else done maybe you could crochet several rows (however many it takes to really get the curl out) of whatever is the main color along the edge and then do whatever they have for the final contrast color.
You are probably not doing anything wrong. If that one row of white crochet is supposed to tame all the curl and nothing else built in to tame it, it probably won't be enough to do the trick. It may not take much more maybe only another row or two.
If the neck of the sweater has something that deals with the curl you could work the crocheted dark borders first (on the fronts) and then do the white all the way around fronts and neck in one row.
Oh, I just thought of another answer. You could pick up stitches along the fronts and knit a ribbed or garter border on and then do the crochet border around that. I didn't notice if you had buttonholes in the body of the sweater. If so that might not work.