Yikes! I mis-read your post. It was about "nesting" and not "twirling".
For important seams, I pin before and after the seam intersection. It holds the fabric in place as it goes through the feed dogs.
What foot are you using on the machine? I learned that some machine feet are just a little wider and help hold the fabric too.
You can also use a dot of school glue and press an iron over the seam. It will hold the intersections in place for stitching. Yes, it takes time but helps in times when you need those perfect seams or points.