Are you able to remove the pieces that are embroidered? It looks like it is not all one piece but meybe sewn on separately. If so try to remove them and do another piece. If that is the case I would not take it back to them. I use wash away stabalizer and if you let it drip dry you don't get any puckers. If you take the embroidery out from front or back it will not only leave holes but faint color of the thread used. If that doesn't work I would do very close stapeling. You might try spray starch and ironing.
Hugs
Loretta