I not only use a two sided stabilizer to bond my design to my base fabric but also something like Totally Stable (a tearaway) on the bottom of the entire block or whatever you are appliquing. You also need to be sure you are using the correct foot for satin stitching as the wrong foot can cause it to not feed correctly. Also you might check the density of your stitching and loosen (widen the length of the stitch) a little til it looks correct.
Hope you can get the puckers out with moistening and pressing. Good Luck!