Shes doing the right thing, she's probably concerned about blood clots in addition, its more common that expected.
In terms of the acne, there's a number of antibiotics that can be tried, Erythromycin, Doxycyline, Lymecyline etc, try them before going on the pill.. If they fail there are topical alternatives, Treclin, Panoxyl, Zineryt and Duac.
As there other alternatives and taking into account the BRCA mutation in the family history, I'd say your doctor is doing the right thing.
Remember he/she went to medical school for 5 years and then spent years on top of that to actually become a GP, have some faith.