The quilt looks very nice. From the picture the floral appears to match. However, since you said that it looks or reads as a lavendar then I would probably keep searching for a fabric to use as the outside border fabric. Since your DGD want flannel for the backing then have flannel as the quilt is for her.
Is it possible to have her help you pick out the fabrics for both the outside border(s) and the backing? This would be best if at all possible. If she's in another city, then mail her fabric swatches and have her look in her area and find what she likes. She can then get the information and a fabric swatch and sent it back to you.
It seems that children really do have strong opinions about what they like. They like bright colors. I would do my best to make it to her liking. She will love that she got to be a part of the quilt making process. Maybe a future quilter's lurking inside?
Pam M