Try looking at some oriental fabrics for ideas how to use the two colors together. I lived in Japan for a time and brought home a kimono that is primarily purple, orange and red chrysanthemums on a white ground, and it's drop-dead gorgeous!
Also consider using those colors in varying intensities. Just a bit of deep purple and red, shading to lilacs and rose or pinks could be breathtaking.
Hope we get to see it when it's finished!