It's perfectly normal for the sides of stockinette stitch to curl. And as long as you're going to be seaming those sides together you'll have no worries because the sides will be seamed together so the curl will be gone!
Check out Amy's videos on some stitches that can be used to do side seams and also consider blocking each piece before you sew them all together for a really professional looking finish for your piece.
Good luck! Let us know how your project comes out!