Have you sewn clothing and worked on sleeves that curve? With quilting pieces that curve, the process is the same. Ease the pieces and pin them well. Then sew slowly. You will also find that clipping the curves helps the curve to lie more smoothly.
When you turn the fabric, be sure the needle is down before you lift the pressure foot; then the fabric won't move and the needle stays in place. My problem is that the needle has a tendency to move even when in the down position. I discovered that I was pulling the fabric when I turned it and moved the needle slightly. If you use a throat plate on the machine that is used for straight stitich only, the needle doesn't move.
Relax and enjoy what you are doing. Who says everything we make has to be perfect? We learn only from our mistakes.
Good luck with your project.
Connie