I can understand how you feel. It doesn't look bad at all, but is not what you were hoping for. I have embroider with my Mom for years, and I hope you don't mind a suggestion. You can still use two shades of purple, but istead of stitching horizontal lines, she did vertical lines starting in the center of the flower, and made sure they didn't all ended on a straight line in the middle of the petal, but made some stitches shorter and some longer, so that the darker color will have also some longer and some shorter, this way it looks more natural. You can do the same thing with the bird, specially in the area of the neck, where there are color changes. I can not see the holes made by the needle, but 3 strands sound like a better choice. I am sure is going to look lovely. Your mother is very lucky. I hope my own daughter someday put half the effort into making something for me.
Maria