Generally you do all the fancy stitching before sandwiching. You can use a buttonhole stitch or similar through the sandwich but you will need to enlarge the stitch length a lot because the thickness will pull up a lot. The drawback of that is the appliqué will not be fastened very securely and you will have the buttonhole stitches visible on the back. For a wall hanging, it might be okay since you will not be washing it.