Ellen,
As you and your daughter pointed out, bipolar is just a label. The important point is treatment and healing. Therapy not necessarily for the label "bipolar" but for specific problems in her life. Treatment CAN be accomplished even if the "label" is rejected.
You may also want to contact the parents at
www.bpkids.org and take a look at Mark Hyman's book and blog:
http://www.ultrawellness.com/blog and Wolfson's as well:
http://www.itsnotmental.com