I'm making a dress out of one-way cotton blend stretch fabric with a one-way stretch lining (meaning they only stretch east to west and not also north to south). I want to put some small cutouts in the front of the dress -- four total. The cutouts will be the shape of diamonds, but with the east-west points rounded so that the only points are on top and bottom. Kind of like a diamond and oval hybrid. I am concerned about sewing these so my material doesn't bunch or become disproportionate. Also, I want to make sure I take care to completely conceal the seams at the points so the fabric doesn't rip.
Do you have any pointers about how to pull these cutouts off so the seams are strong and completely concealed,
Your cutout sounds great, and done right, not too much of a challenge.
You can easily achieve the look you want without compromising the strength of the fabric/garment by reinforcing the cutout seam. Normally I would stitch a cotton tape into the seam for reinforcement, but as you are using a stretch faric, you could choose to use an elastic for a little more give. Stitch the edge of the elastic into the cutout seam as you work it (right sides together then turn through the hole) and snip to the stitching line at the points.
Use 2 pieces of elastic, one for each side of the cutout, so that the ends run off the seams at the top and bottom. If you turn the corner with the elastic, it may interfere with the way the cutout corners sit, so running the ends off gives a better finish. Use a small stitch length at the points as there won't be much fabric once you snip to the stitching line, so you don't want to give the knit a chance to unravel past the seam.
And as always... test it before you put it into your garment. You can play around with edgestitching the seam towards the lining to give better flat finish after the seam is finished, or you may be happy with the finish after just a good pressing. Try it out on a scrap and decide for yourself :)
Happy sewing! :)