did you fuse those pieces on? if so they will fray if not sewn down around the edges. I mean a tight stitch around them not just a running stitch. It should perhaps be a wall quilt and you make something else that is pieced for her. I find applique is not for a lot of washing. I am so sorry she is not happy with it. I think she should also learn to be thankful for her gift. you tried, lessons learned and all that the gift was made with your love and time. I don't believe other than a whole of stitching is done that you can solve this problem this time. ..next year maybe a nice color blocked quilt in her favorite colors to use til its threads again. (this is what little ones do).