If the black woman feels she is on a broken treadmill, she has cause. These numbers may well explain why the black woman supervisor may face special problems with white female subordinates. The white woman, accustomed to dealing with white supervisors and used to black women only in lesser positions, may be both confused and hostile. She may also set herself up as your keenest competitor. If she attempts to circumvent you, you should employ the same methods put forth for dealing with rebellious males.
Passive aggression is a coping mechanism of people at odds with someone in a position of authority.
Its tactics are sullenness, sarcasm, procrastination, and deliberate inefficiency, all of which can be difficult to document. The passive aggressor knows this but also knows that you are aware of what's going on. She will take pains to make sure you know. One way to resolve the conflict is to invite her in for a discussion of specific incidents that you find unacceptable without openly accusing her of passive aggression. Discuss ways to improve the quality of her work and set a reasonable deadline by which you want to see an improvement.