My son took AP Chem and he also goes to a high school where AP tests are required for all students who take the corresponding class. This information is made very clear to students and parents before they elect the AP class. I don't know if anyone has ever challenged the policy and … if so … what the outcome was when they did … or how much legal wrangling was involved.
But here are a few thoughts:
1. You can pursue this with the school administration but, if they are firm about the test requirement, you might have to enlist a lawyer, which will end up costing a lot more than an AP test will cost. (But if the high school did not make the test requirement clear before enrollment, you will be in better shape to contest it.)
2. If your daughter does not take the AP test and thus does not report a score to colleges, some admission officials will wonder WHY she didn't report a score (especially if they are aware of the mandatory-test policy at her high school.) It could reflect poorly on her because they will assume that she got a bad score. Of course, she can use the “Additional Information" section of her applications to explain that she didn't take the test for financial reasons and also because she had no need for the chemistry credits in college. Colleges may or may not accept this reason as valid. And their view of it might depend on their cursory assessment of your household finances. For instance, a student from a single-parent home with an unemployed mother will be regarded differently than a student from a home with two professional parents. In the latter case, the college folks may question the validity of your daughter's excuse and this could work against her … at least in some small way.
3. The fact that your daughter will have to repeat chemistry in college will have little bearing on this issue, if you knew up front that the AP test was required. In addition, if she earns a high score on this exam, most (though not all) colleges will count these credits and they don't necessarily have to replace a chemistry class. In other words, your daughter would walk through the college gates on Day One with college credits under her belt and she might be able to use these credits later on to make up a failed class in another area or to compensate for any shortfall that occurs for a range of reasons. Colleges have widely varying policies when it comes to the ways they allow students to use AP credits, so your daughter's choice of school will obviously affect the value of the credits she might earn from faring well on the AP Chem exam.
Bottom line: if it were my own son in this situation, I would tell him to take the test. But if the money is a serious concern, go to the high school officials first and see what they recommend. You can also try asking other CC members on the Parents forum if they were ever in this situation and how it played out.
Sorry that I can't give you better news, but I think that you may be on thin ice with this one.