Would it work to fill out the paperwork to homeschool them officially, and then just send them to college? You'd have to look into the regulations for taking the GED as homeschoolers; these regs must exist (do any of you homeschoolers know)?
Also, if all else fails, write a detailed letter to the principal asking for written explicit answers to explicit questions. Make them work hard to justify the denial and they might give in to avoid the hassle.
For example:
1. Please tell us exactly why you will not give credit for courses approved not only by Jane's last school, but also by <name of local college/university>.
Jane's syllabus and assignments from <course name and number> are attached, as is her transcript showing that she passed the course. Please enumerate the problems with the course and how they do not fulfill the requirements of your high school so that we can help her bridge the gaps in her learning.
2. We have been told that the calculus course at the college is more rigorous than the AP course at the high school.
Do you have information showing that our information is incorrect? We are new to this area and are not aware of the weaknesses of local colleges. If indeed the calculus courses at the college are of substandard quality, please enumerate their deficiencies so that we will be able to avoid problematic courses in the future.
Etc. etc. Then write a nice syrupy closing paragraph thanking them for helping you.
This approach has helped us in the past with our younger kids.
Val