How fortunate your daughter is to have such an insightful mother. Your concerns about peer pressure, and academics centered around passing state-mandated tests, are certainly valid.
Let us first compare the possibilities in using High School of Your Dreams, or a pre-packaged format, in light of your daughter's struggles with math and science.
A pre-packaged program will likely offer you two options: place your daughter at levels in math and science that are above her abilities so that she continues to struggle, or place her below level in those subjects so that she might catch up BUT demand so much in other courses that school will still be overwhelming for her.
High School of Your Dreams, on the other hand, allows you to tailor not only her math and science courses to fit her needs, but also to tailor her other subjects as well, until she is able to catch up. At the same time, HSYD will allow your daughter to pursue her interests in music and dance and, if you are located near any type of marine science facility [like Sea World] may show her ways to access volunteer opportunities in her areas of interest.
Making the leap into homeschooling sometimes seems as frighteningly adventuresome as homesteading the moon. When taking such a 'leap of faith,' it is instinctive to want as much guidance as possible! Hence, it is natural to reach for a pre-packaged program that mandates every subject, text, assignment, and test.
However, if the pre-packaged program doesn't fit, little has been gained and much can be lost. In all fairness to pre-packaged providers, some will truly attempt, over time, to adjust the program to fit the needs of the student. Yet, if it is through observing the student struggle over a period of weeks or months that experimental adjustments are made--and adjustments mean dropping the current plan and moving to another book or course, which means the student must begin again--how is having a pre-packaged program an improvement over making those decisions within your own home, before your daughter begins to struggle again? You, as mom, know your daughter far better than anyone outside the family. With a pre-packaged program, it would be your input, passed on to a counselor, that would be 'filtered' by another, to create yet another program for your daughter. How much better if your input is not 'filtered,' but applied by you, in discussion with your daughter, to design a program that will truly fit her abilities and needs, from the beginning. Using this approach, your daughter can begin high school with success, not failure.
May I encourage you to learn more about High School of Your Dreams and then talk with your daughter about the possibilities that might be open to her with this program?
Finally, Our Lord has blessed your family with this daughter, and gifted you with insight. It seems to me that He is already preparing you to take this wonderful adventure with your daughter. Pray for His guidance, and He will provide it. In the meantime, you are in our prayers, as well.
May God bless and guide your homeschooling journey,